Browse Vector problems Studdy Solved!

Problem 201

Sketch the figure for $\ddot{XY} \perp \overrightarrow{YZ}$ . What’s the first step: A, B, C, or D?

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Problem 202

Find point $B$ on line segment $\overline{AC}$ such that the ratio $AB : AC = 1 : 3$ where $A=(-2,4)$ and $C=(4,7)$ .

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Problem 203

Srient $A(3 ; 5) ; B(-1 ;-7)$ e $C(-1 ; 1)$ Deteriminer les cordonnées duvectewis $\overrightarrow{A B}$ . Déterminer une équation cortésienne de fo droté ( $A B$ ) 3) Déterminer une équation caratésienne de lo drote 10) passont par $C$ et pexpendiculaire à $(A B)$ .

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Problem 204

Let $\vec{F}=5(x+y) \vec{i}+4 \sin (y) \vec{j}$ . Find the line integral of $\vec{F}$ around the perimeter of the rectangle with corners $(3,0),(3,5),(-1,5),(-1,0)$ , traversed in that order. line integral =

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Problem 205

Suppose that $\|\vec{v}\|=22$ and $\|\vec{w}\|=6$ . Suppose also that, when drawn starting at the same point, $\vec{v}$ and $\vec{w}$ make an angle of $\frac{5 \pi}{6}$ radians. (A.) Find $\|\vec{w}+\vec{v}\|$ and round to two decimal places. $\|\vec{w}+\vec{v}\|=\square$ (B.) Find $\|\vec{w}-\vec{v}\|$ and round to two decimal places. $\|\vec{w}-\vec{v}\|=\square$

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Problem 206

Resolve the vectors shown in the figure below into components. (Here, the vectors $\vec{i}=\mathbf{i}$ and $\vec{j}=\mathbf{j}$ .) $\begin{array}{l} \vec{a}=\square \mathbf{i}+\square \mathbf{j} \\ \vec{b}=\square \mathrm{i}+\square \mathrm{j} \\ \vec{v}=\square \mathrm{i}+\square \mathrm{j} \\ \vec{w}=\square \mathrm{i}+\square \mathrm{j} \end{array}$

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Problem 207

1. Find the midpoint of $\overline{B D}$ where B is at $(-5,-6)$ and D is at $(9,11)$ .
2. If M is the midpoint of $\overline{X Y}$ with $X(1,-2)$ and $M(7,4)$ , find Y's coordinates.
3. Calculate the length of $\overline{R S}$ for $R(8,2)$ and $S(3,7)$ , rounding to the nearest whole number.
4. Find the weighted average of 6 (weight 4) and 12 (weight 2).

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Problem 208

Vector $\mathbf{v}$ has initial point $P(11,12)$ and terminal point $Q(19,-1)$ . Vector $\mathbf{w}$ has initial point $R(7,12)$ and terminal point $S(-1,-1)$ .
Part: $0 / 3$ $\square$
Part 1 of 3 (a) Find the magnitude of $\mathbf{v}$ . Give the exact answer in simplest form. $\|\mathbf{v}\|=$ $\square$ $\sqrt{\square}$

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Problem 209

What is angle for the point $M(-1,0)$ ?
A 270 B -90
C 90 D 180
SUBMIT ANSWER

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Problem 210

arx Maths 1 A 18 $1 c$ 1D $1 E$ Summary Bookwork code: IA Calculator not allowed
What are the coordinates of the point halfway between the origin and point $A$ on the coordin Zoom

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Problem 211

13 Diberi segi tiga $A B C$ dengan $\overrightarrow{A B}=4 \underset{\sim}{i}-6 \underset{\sim}{j}$ dan $\overrightarrow{A C}=2 \underset{\sim}{i}+4 \underset{\sim}{j} . T$ berada pada garis $B C$ dengan keadaan $3 B T=T C$ . It is given that a triangle $A B C$ with $\overrightarrow{A B}=4 \underset{\sim}{i}-6 \underset{\sim}{j} \underset{\sim n d}{A C}=2 \underset{\sim}{i}+4 \underset{\sim}{j}$ . T lies on the line $B C$ such that $3 B T=T C$ . (a) Cari vektor Find the vector (i) $\overrightarrow{B C}$ , (ii) $\overrightarrow{A T}$ . Seterusnya, car1 vektor unit dalam arah $\overrightarrow{A T}$ . $\overrightarrow{A T}$ . Hence, find the unit vector in the direction of $\overrightarrow{A T}$ . [5 markah] [5 marks] (b) Jika $D$ ialah satu titik dengan keadaan $\overrightarrow{A D}=h \overrightarrow{B C}$ dan $\overrightarrow{A D}=-3 \underset{\sim}{i}+\underset{\sim}{k j}$ , dengan keadaan $h$ dan $k$ adalah pemalar. Cari nilai $h$ dan nilai $k$ . If $D$ is a point such that $\overrightarrow{A D}=h \overrightarrow{B C}$ and $\overrightarrow{A D}=-3 i \underset{\sim}{i}+k$ , such that $h$ and $k$ are constants. Find the value of $h$ and of $k$ .

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Problem 212

Are the following statements true or false?
False
1. For any scalar $c$ and any vector $\vec{v}$ , we have $\|c \vec{v}\|=c\|\vec{v}\|$ .
False
2. If $\vec{v}$ and $\vec{w}$ are any two vectors, then $\|\vec{v}+\vec{w}\|=\|\vec{v}\|+\|\vec{w}\|$ .
False
3. $(\vec{i} \times \vec{j}) \cdot \vec{k}=\vec{i} \cdot(\vec{j} \times \vec{k})$ .
True
4. The value of $\vec{v} \cdot(\vec{v} \times \vec{w})$ is always zero.

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Problem 213

Let $P=(0,0,0), Q=(1,-1,-1), R=(-2,1,1)$ . Find the area of the triangle $P Q R$ . area $=$ $\square$ Let $T=(4,4,1), U=(9,7,7), V=(-6,7,1)$ . Find the area of the triangle $T U V$ . area = $\square$

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Problem 214

Determine the direction of the resultant of the following vectors with the $\mathrm{x}-\operatorname{axis}\left(\theta_{\mathrm{x}}\right)$ : $\begin{array}{l} \boldsymbol{A}=3 \hat{\imath}+7 \hat{\jmath}+8 \hat{k} \\ \boldsymbol{B}=4 \hat{\imath}-5 \hat{\jmath}+3 \hat{k} \\ \boldsymbol{C}=2 \hat{\imath}+3 \hat{\jmath}-4 \hat{k} \end{array}$ $95^{\circ}$ b. $55.8^{\circ}$ $66.3^{\circ}$ $43.7^{\circ}$

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Problem 215

Given $\vec{u}=[-1,2,-1], \vec{v}=[-4,3,-2]$ and $\vec{w}=[3,2,-2]$ , find (i) $u-3 \vec{v}+2 \vec{w}$ $=[3(-4) ; 3(3) ; 3(-2)]=[-12 ; 9 ;-6]$

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Problem 216

Consider the following vectors: $\mathbf{a}=\left[\begin{array}{c} 1 \\ 2 \\ -3 \\ -1 \end{array}\right] \quad \mathbf{b}=\left[\begin{array}{c} 1 \\ 4 \\ -1 \\ -2 \end{array}\right] \mathbf{c}=\left[\begin{array}{c} 2 \\ -2 \\ -10 \\ -1 \end{array}\right]$
For each of the following vectors, determine whether it is in $\operatorname{span}\{\mathbf{a}, \mathbf{b}, \mathbf{c}\}$ . If so, express it as a linear combination using $a, b$ , and $c$ as the names of the vectors above. $\mathbf{v}_{1}=\left[\begin{array}{c}2 \\ -4 \\ -12 \\ 0\end{array}\right]$ < Select an answer > $\mathbf{v}_{2}=\left[\begin{array}{c}-2 \\ -8 \\ 2 \\ 4\end{array}\right] \quad$ Select an answer > $\mathbf{v}_{3}=\left[\begin{array}{c}-10 \\ 2 \\ 6 \\ -6\end{array}\right]$ < Select an answer >

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Problem 217

Which coordinates for points $A^{\prime}$ and $B^{\prime}$ show that lines $AB$ and $A^{\prime}B^{\prime}$ are perpendicular?
1. $A^{\prime}:(p, m)$ and $B^{\prime}:(z, w)$
2. $A^{\prime}:(p, m)$ and $B^{\prime}:(z,-w)$
3. $A^{\prime}:(p,-m)$ and $B^{\prime}:(z, w)$
4. $A^{\prime}:(p,-m)$ and $B^{\prime}:(z,-w)$

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Problem 218

Find the pre-image of vertex $A^{\prime}(8,5)$ after reflection across the $y$ -axis. Options: $(-8,-6)$ , $(-6,8)$ , $(8,6)$ , $(6,-8)$ .

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Problem 219

Find which reflection of the segment from $(-4,-6)$ to $(-6,4)$ gives endpoints $(4,-6)$ and $(6,4)$ .

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Problem 220

Combine the following translations into a single translation:
21. $T_{\langle-3,3\rangle} \circ T_{\langle-2,4\rangle}$
22. $T_{\langle-4,-3\rangle} \circ T_{\langle 3,1\rangle}$
23. $T_{\langle 5,-6\rangle} \circ T_{\langle-7,5\rangle}$
24. $T_{\langle 8,-2\rangle} \circ T_{\langle-4,9\rangle}$

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Problem 221

Find the midpoint of the line segment with endpoints $K(7,7)$ and $L(1,3)$ . Choose from the options: A. $(-3,-2)$ B. $(3,-2)$ C. $(-3,2)$ D. $(3,2)$ .

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Problem 222

If $\|\mathbf{v}\|=2.4$ and $\|\mathbf{w}\|=4$ and the angle between $\mathbf{v}$ and $\mathbf{w}$ is $60^{\circ}$ , find $\mathbf{v} \cdot \mathbf{w}$ . Give an exact answer. $\mathbf{v} \cdot \mathbf{w}=$ $\square$ $\sqrt{\square}$

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Problem 223

4. An airplane is travelling at $500 \mathrm{~km} / \mathrm{h}$ due south when it encounters a win from $W 45^{\circ} \mathrm{N}$ at $100 \mathrm{~km} / \mathrm{h}$ . a. What is the resultant velocity of the airplane? b. How long will it take for the airplane to travel 1000 km ?

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Problem 224

13. Ein U-Boot beginnt eine Tauchfahrt in $\mathrm{P}(100|200| 0)$ mit 11,1 Knoten in Richtung des Peilziels $Z(500|400|-80)$ , bis es eine Tiefe von 80 m erreicht hat. $\left(1 \text { Knoten }=1 \frac{\text { Seemeile }}{\text { Stunde }} \approx 1,852 \frac{\mathrm{~km}}{\mathrm{~h}}\right)$
Anschließend geht es ohne Kurswechsel in eine horizontale Schleichfahrt von 11 Knoten ein. Könnte es zu einer Kollision mit der Tauchkugel T kommen, die zeitgleich vom Forschungsschiff $S(700|800| 0)$ mit einer Geschwindigkeit von $0,5 \frac{\mathrm{~m}}{\mathrm{~s}}$ senkrecht sinkt?

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Problem 225

13. Ein U-Boot beginnt eine Tauchfahrt in $\mathrm{P}(100|200| 0)$ mit 11,1 Knoten in Richtung des Peilziels $Z(500|400|-80)$ , bis es eine Tiefe von 80 m erreicht hat. $\left(1 \text { Knoten }=1 \frac{\text { Seemeile }}{\text { Stunde }} \approx 1,852 \frac{\mathrm{~km}}{\mathrm{~h}}\right)$
Anschließend geht es ohne Kurswechsel in eine horizontale Schleichfahrt von 11 Knoten ein. Könnte es zu einer Kollision mit der Tauchkugel T kommen, die zeitgleich vom Forschungsschiff $S(700|800| 0)$ mit einer Geschwindigkeit von $0,5 \frac{\mathrm{~m}}{\mathrm{~s}}$ senkrecht sinkt?

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Problem 226

Найди координаты вершины K параллелограмма MNKL, если $\mathrm{M}(-6 ;-2), \mathrm{N}(-2 ; 2)$ и $\mathrm{L}(1 ;-2)$ .
Запиши числа в поля ответа. $\mathrm{K}(\square ; \square)$
Осталась 1 попытка
Готово

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Problem 227

Найди координаты вершины N параллелограмма MNKL, если $\mathrm{M}(-3 ;-1), \mathrm{K}(5 ; 4)$ и $\mathrm{L}(2 ;-1)$ .
Запиши числа в поля ответа. $\square$ $\square$ )

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Problem 228

Question 5 of 18 This test: 18 point(s) possible This question: 1 point(s) possible
Use the figure to evaluate $\mathbf{a}+\mathbf{b}, \mathbf{a}-\mathbf{b}$ , and $-\mathbf{a}$ $\begin{array}{c} \mathrm{a}+\mathrm{b}=\langle\square, \square\rangle \\ \mathrm{a}-\mathrm{b}=\langle\square, \square\rangle \\ -\mathbf{a}=\langle\square, \square\rangle \end{array}$

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Problem 229

Give a vector parametric equation for the line through the point $(-1,0,4)$ that is parallel to the line $\langle 4-5 t, 4-4 t, 5-2 t\rangle$ : $L(t)=$

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Problem 230

10.5. Which of the following statements are true? A) Let $\mathbf{u}$ and $\mathbf{v}$ be any two vectors in $\mathbb{R}^{n}$ . Then $\mathbf{u} \cdot \mathbf{v} \geq 0$ . B) Let $\mathbf{u}$ and $\mathbf{v}$ be vectors in $\mathbb{R}^{n}$ such that $\mathbf{u} \cdot \mathbf{v}<0$ . Then $\mathbf{u}=-c \mathbf{v}$ , for some scalar $c>0$ . C) Let $\mathbf{u}$ and $\mathbf{v}$ be vectors in $\mathbb{R}^{n}$ and let $\theta, 0 \leq \theta \leq \pi$ be the angle between them. If $\mathbf{u} \cdot \mathbf{v}<0$ , then $\frac{\pi}{2}<\theta \leq \pi$ . D) Let $\mathbf{u}$ and $\mathbf{v}$ be vectors in $\mathbb{R}^{n}$ such that $\mathbf{u} \cdot \mathbf{v}=0$ . Then either $\mathbf{u}=\mathbf{0}$ or $\mathbf{v}=\mathbf{0}$ .

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Problem 231

10.6. Find the angle $\theta, 0 \leq \theta \leq \pi$ between the vectors $\mathbf{u}=\left[\begin{array}{r} 1 \\ -2 \\ 2 \end{array}\right] \text { and } \mathbf{v}=\left[\begin{array}{r} -2 \\ 2 \\ 1 \end{array}\right]$

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Problem 232

Si $\vec{u}=[3,4]$ et $\vec{v}=[6, k]$ , quelle est la valeur de $k$ si les deux vecteurs sont orthogonaux.

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Problem 233

Find the midpoint of the segment with endpoints $(-2,3)$ and $(5,-3)$ .

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Problem 234

Identify the opposite ray to $\overrightarrow{N M}$ from the options: $\overrightarrow{N O}$ , $M$ , $\overrightarrow{N P}$ , $\overrightarrow{M P}$ , or all of the above.

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Problem 235

Find the midpoint of the segment with endpoints $(-9,-2)$ and $(-1,-8)$ .

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Problem 236

Find the coordinates that divide the line segment from $(2,-6)$ to $(5,6)$ in a 1:5 ratio.

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Problem 237

MathXL for School: Practice and Problem-Solving
Points $A^{\prime}$ and $B^{\prime}$ are images of points $A$ and $B$ after a $270^{\circ}$ rotation about the origin. If the slope of $\overrightarrow{A B}$ is -3 , what is the slope of $\widehat{A^{\prime} B^{\prime}}$ ? Explain.
Select the correct choice below and fill in the answer box to complete your chaice. A. A rotation of $270^{\circ}$ would result in a line parallel to $\overrightarrow{A B}$ . Since the slopes of parallel lines are equal, the slope of $\overrightarrow{\mathrm{A}^{\prime} B^{\prime}}$ is $\square$ 1. B. A rotation of $270^{\circ}$ would result in a line perpendicular to $\overrightarrow{\mathrm{AB}}$ . Since the slopes of perpendicular lines are opposite reciprocals, the slope of $\overrightarrow{\mathrm{A}^{\prime} \mathrm{B}^{\prime}}$ is $\square$ . C. A rotation of $270^{\circ}$ would result in a line perpendicular to $\overrightarrow{A B}$ . Since the slopes of perpendicular lines are equal, the slope of $\overrightarrow{A^{\prime} B}$ is $\square$ . D. A rotation of $270^{\circ}$ would result in a line parallel to $\overrightarrow{A B}$ . Since the slopes of parallel lines are opposite reciprocals, the slope of $\overrightarrow{A^{\prime} B}$ is $\square$

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Problem 238

Hilfsmittelteil (erlaubte Hilfsmittel: graphikfähiger Taschenrechner, Formelsammlung) Aufgabe 4: (37 Punkte) Die Abbildung zeigt den Würfel ABCDEFGH mit $\mathrm{G}(5|5| 5)$ und $\mathrm{H}(0|5| 5)$ in einem kartesischen Koordinatensystem. Die Punkte I(5|0|1), J(2|5|0), $\mathrm{K}(0|5| 2)$ und $L(1|0| 5)$ liegen jeweils auf einer Kante des Würfels.
8 多 (2P) - $A$ - e) Zeigen Sie, dass das Viereck IJKL ein Trapez ist, in dem zwei Seiten gleich lang sind. Weisen Sie nach, dass die Seite $\overline{\mathrm{L}}$ des Trapezes doppelt so lang ist wie die Seite JK. (7P) f) Berechnen Sie die Größe eines Innenwinkels des Trapezes IJKL. (6P) (4P)
Der Punkt P (4|0|2) liegt auf der Strecke $\overline{\mathrm{IL}}$ . Die Strecke $\overline{\mathrm{JP}}$ steht dabei senkrecht zur Strecke $\overline{\mathrm{IL}}$ . g) Berechnen Sie den Flächeninhalt des Trapezes IJKL. (5P) h) Gegeben ist die Ebene $S: \vec{x}=v \cdot\left(\begin{array}{c}-1 \\ -5 \\ 5\end{array}\right)+w \cdot\left(\begin{array}{c}-5 \\ 5 \\ 1\end{array}\right)$ mit $v, w \in \mathbb{R}$ .
Der Punkt K liegt in einer Ebene T, die parallel zu S ist. Untersuchen Sie, ob auch der Punkt L in T liegt. (5P)

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Problem 239

(A) Find the parametric equations for the line through the point $\mathrm{P}=(5,-5,3)$ that is perpendicular to the plane $1 x+3 y+4 z=1$ . $\begin{array}{l} x=\square \\ y=\square \\ z=\square \end{array}$ (B) At what point $Q$ does this line intersect the $y z$ -plane? $\mathrm{Q}=(\square, \square)$ $\square$

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Problem 240

Si un système est en mouvement rectiligne: (If a system is in rectilinear motion
Select one or more: Sa trajectoire est une droite. (Its trajectory is a straight line.) La norme de sa vitesse est constante. (The norm of its speed is constant) Le vecteur vitesse peut varier. (The velocity can vary)
Check

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Problem 241

Le vecteur vitesse $v(t)$ est: (The velocity vector $v(t)$ is
Select one or more: La dérivée par rapport au temps t du vecteur accélération a(t). (The derivative with respect to time $t$ of the acceleration vector $a(t)$ . La dérivée par rapport au temps $t$ du vecteur position $O M(t)$ . (The derivative with respect to time $t$ of the position vector $O M(t)$ .) Toujours tangent à la trajectoire au point consideré. (Always tangent to the trajectory at the point considered)

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Problem 242

Given $\mathbf{u}_{1}=(6,-1)$ and $\mathbf{u}_{2}=(3,2)$ , if we let $\mathbf{v}_{1}=\mathbf{u}_{1}$ , use the Gram-Schmidt process to find $\mathbf{v}_{2}$ If needed, enter your answers as fractions, not decimals.
This question accepts'answers that are in a form like " $(-1,3)$ " or " $(3,7,3 z)$ ". The entries can be numbers or formulas. Help | Preview

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Problem 243

1 point
Given $\bar{p}=2 x+1 x^{2}$ , find the norm of $p$

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Problem 244

- Question 3
1 point Number Help
Find $<5 \bar{u}, 5 \bar{v}+2 \bar{w}>$ , given that $<\bar{u}, \bar{v}>=4,<\bar{v}, \bar{w}>=-5$ , and $<\bar{u}, \bar{w}>=-2$ Number

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Problem 245

، C( 32,24 $)$ , A( 0,0 $)$ هو مُعيّن. معطى: ABCD (18) . الزَأس B يقع على الشّعاع الموجب المحور ABCD (ب) طول ضلع المعيّن هو 25 وحدة طول.
جدوا إحداثيّات النّقطة D. (ج) إحسبوا طول قطر المُعيّن الأصغر.

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Problem 246

36. (II) Two large snowcats are towing a housing unit north, as shown in Fig. 4-42. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ exerted on the unit by the horizontal cables is north, parallel to the line L, and $F_{\mathrm{A}}=4200 \mathrm{~N}$ . Determine $F_{B}$ and the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .
FIGURE 4-42 Problem 36.

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Problem 247

42. (II) A 3.0-kg object has the following two forces acting on it: $\begin{array}{l} \overrightarrow{\mathbf{F}}_{1}=(16 \hat{\mathbf{i}}+12 \hat{\mathbf{j}}) \mathbf{N} \\ \overrightarrow{\mathbf{F}}_{2}=(-10 \hat{\mathbf{i}}+22 \hat{\mathbf{j}}) \mathbf{N} \end{array}$
If the object is initially at rest, determine its velocity $\overrightarrow{\mathbf{v}}$ at $t=4.0 \mathrm{~s}$ .

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Problem 248

Find the area of the parallelogram with vertices at (-4,-5), (3,-3), (-4,-9), (3,-7).

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Problem 249

Several unit vectors $\vec{r}, \vec{s}, \vec{t}, \vec{u}, \vec{n}$ , and $\vec{e}$ in the xy-plane (not threedimensional space) are shown in the figure.
Using the geometric definition of the dot product, are the following dot products positive, negative, or zero? You may assume that angles that look the same are the same. $\square$ 1. $\vec{n} \cdot \vec{e}$ ? ? ? ? $\square$ ? $\square$ ? ? $\square$
2. $\vec{s} \cdot \vec{t}$ (Click on graph to enlarge)

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Problem 250

Find the midpoint of the line segment with the given endpoints. $(-6,-3) \text { and }(-1,-5)$
The midpoint is $\square$ (Type an ordered pair.)

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Problem 251

11. Solve the followings; a) Given that $\mathrm{P}(-3,4)$ . Calculate the unit vector in the direction of $\overrightarrow{\mathrm{OP}}$ Ans: $\frac{-3 i+4 j}{5}$ b) Given that vectors $\overrightarrow{O P}=-1 i-5 j-11 k$ and $\overrightarrow{O R}=-4 i-2 j+3 k$ .
Express the vectors of $\overrightarrow{P R}$ . Ans: $-3 i+3 j+14 k$

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Problem 252

11. Three vectors are given by $\vec{P}=3 i-3 j-2 \hat{K}, \vec{Q}-i-j i+2 \mathrm{~K}$ and $\vec{S}=2 \mathrm{i}+2 \mathrm{j}+\mathrm{K}$ . Then get $2 \vec{P} \cdot(3 Q+\vec{S}) ? 6 i-6 j-4 k \cdot(-3 i+12 j+6 k+2 i+2 j+k)$
12. For what value of $\vec{C}$ lying along +y-axis does $\vec{A} \cdot(\vec{Q}-\vec{C})=0$ given that $\vec{A}-3 i-2 j+k$ and $\vec{B}=4 i+5 j+7 k$ ? ） $(-i-10 j+7 k)$
13. Given that $\vec{P}=5 i-6 \mathrm{j}, \vec{Q}=-2 i+3 \mathrm{j}$ and $\vec{R}$ lies in the xy plane perpendicular to $\vec{P}$ 15 If the dot product of $\vec{R}$ and $\vec{Q}$ is 9 . Then get $\vec{R}$ ? $\vec{R} \vec{Q} \overrightarrow{=}=R_{x} Q_{x}+R_{y} Q_{y}$
14. Find $\vec{R}=\mathrm{a} i+\mathrm{bj}+\mathrm{k}$ which is perpendicular to both $\vec{A}=3 i+j-\mathrm{K}$ and $+3 R_{y}$ $\vec{B}=-3 i+2 j+2 k$ . $5 R_{x}-6 R_{y}=0 \quad 4 i-1 / 3 d$
15. Let $\vec{A}=i+j+\hat{K}$ and $\vec{B}=2 i+2 j+2 \mathrm{k}$ what is the angle between $\vec{A}$ and $\vec{B}$ ?
16. Find a such that, the angle between $\vec{A}=i+a j$ and $\vec{B}=i+j$ is $45^{\circ}$ . ( $\sin 45^{\circ}=$ $\left.\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)$ it $\sqrt{2}$ $\vec{B}=\stackrel{\alpha}{\alpha i-3 \propto j+5 k}$ orthogonal
17. For what value of $\propto$ are the vectors $\vec{A}=\alpha i-2 j+\hat{k}$ and $\vec{B}=a i-3 \propto j+5$ to each other? $\quad \alpha=-1$ or $\alpha=-5-i-2 j+k \quad-i+3 j+5$
18. Consider a block placed on a horizontal surface and that force $\vec{F}$ is applied on the block to move the block through displacement $\vec{S}$ . If $\vec{F}=(5 i+3 j) N$ and $\vec{s}=(-2 i+4 j) \mathrm{m}$ then calculate the work done? $\quad-5 i-2 j+k \quad 5 i+1 s j+5$ 19.Vector $\vec{A}$ has a magnitude of 6 units along the positve $x-25-30$ , Vector $\vec{B}$ has amagnitude of 4 units and lies on xy-plane making an angle of $60^{\circ}$ with the positive x -axis. What is the scalardot product of $\vec{A}$ and $\vec{B}$ ? 20. i.If $\vec{A} \cdot \vec{B}=|A||B|$ , what can you say about vector $\vec{A}$ and $\vec{B}$ ? ii. if $\vec{P}+\vec{Q}=O$ , then tell about vectors $\vec{P}$ and $\vec{Q}$ ? iii. use the given diagram and express $\vec{N}, \vec{M}$ and $\vec{Z}$ interns of $\vec{Q}$ ? $\begin{array}{c} -36+3 R y=9 \\ R_{y}=15 \\ 18 i+15 y= \\ 18 \\ (\alpha+1)(\alpha+5) \\ \alpha^{2}+6 \alpha+5 \end{array}$

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Problem 253

(6.) Für ein Dreeick $A B C$ gilt: $A(3 /-2), A B=(1 / 2), A C=(-1 / 1)$ . Geben Sie die Koordinalen des Schwerpunkts $S$ des Dreiecks an.
9. Geben Sie die in kartesischer Binomialform gegebenen Punkte in Polarform an. $A(-5 /-2), B(0 / 5), C(-6 / 0), D(-6 / 3)$

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Problem 254

horizontal 1.10 A stunt rider is propelled upward from his motorbike by a spring loaded ejector seat. The rider was travelling horizontally at $60 \mathrm{~km} \mathrm{~h}^{-1}$ when the ejector seat was triggered, and as they leave the seat they are travelling with a vertical velocity of $15 \mathrm{~m} \mathrm{~s}^{-1}$ . The seat is 1.0 m off the ground. (a) What is the initial velocity of the stunt rider (in $\mathrm{km} \mathrm{h}^{-1}$ )? (b) How high does the stunt rider reach? (c) How far along the track does the stunt rider land on the ground? (d) What is the velocity of the stunt rider when they hit the ground (in $\mathrm{km} \mathrm{h}^{-1}$ )?

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Problem 255

Graph the reflection of the point $T(10,-2)$ over the $x$ -axis.

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Problem 256

Reflect the point $S(0,2)$ over the $x$ -axis. What are the coordinates of $S^{\prime}$ ?

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Problem 257

Exercice 01 : Detx points $A$ et $B$ , ont pour coordonnées cartésiennes dans l'espace : $A(2,3,-3), B(5,7,2)$ Déterminer les composantes du vecteur $\overrightarrow{A B}$ ainsi que son module, sa direction et son sens.

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Problem 258

Exercice 01 : Detx points $A$ et $B$ , ont pour coordonnées cartésiennes dans l'espace : $A(2,3,-3), B(5,7,2)$ Déterminer les composantes du vecteur $\overrightarrow{A B}$ ainsi que son module, sa direction et son sens.

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Problem 259

Exercice 02 : La résultante de deux forces $\vec{F}_{1}$ et $\vec{F}_{2}$ est égale à 50 N et fait un angle de $30^{\circ}$ avec la force $F_{1}=15 \mathrm{~N}$ . Trouver le module de la force $\vec{F}_{2}$ et l'angle entre les deux forces.

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Problem 260

Soient les vecteurs suivants : $\overrightarrow{U_{1}}=A_{1} \vec{i}+A_{2} \vec{j}+A_{3} \vec{k}$ et $\quad \overrightarrow{U_{2}}=B_{1} \vec{i}+B_{2} \vec{j}+B_{3} \vec{k}$ 1) Calculer les produits scalaires : $\vec{U}_{1} \cdot \vec{U}_{2}, \vec{U}_{1} \cdot \vec{U}_{1}, \vec{U}_{2} \cdot \vec{U}_{2}$ ,
On donne: $\vec{V}_{1}=2 \vec{i}-\vec{j}+5 \vec{k}, \vec{V}_{2}=-3 \vec{i}+1,5 \vec{j}-7.5 \vec{k}, \quad \vec{V}_{3}=-5 \vec{i}+4 \vec{j}+\vec{k}$ 2) Calculer $\vec{V}_{1} \cdot \vec{V}_{2}$ et $\vec{V}_{1} \wedge \vec{V}_{2}$ ; 3) Sans faire de représentation graphique que peut-on dire du sens et de la direction du vecteur $\vec{V}_{2}$ par rapport à $\vec{V}_{1}$ ; 4) Calculer les produits suivants $\vec{V}_{1} \cdot\left(\vec{V}_{2} \wedge \vec{V}_{3}\right)$ et $\vec{V}_{1} \wedge\left(\vec{V}_{2} \wedge \vec{V}_{3}\right)$ ; 5) Déterminer la surface du triangle formé par les vecteurs $\vec{V}_{2}$ et $\vec{V}_{3}$

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Problem 261

Soient les vecteurs: $\vec{U}=2 \vec{i}+6 \vec{k}, \vec{V}=8 \vec{i}+y \vec{j}+z \vec{k}, \vec{P}=3 \vec{i}-4 \vec{j}+2 \vec{k}, \vec{Q}=-2 \vec{i}+y \vec{j}+12 \vec{k}$ 1) Déterminer yet $z$ pour que les vecteurs $\vec{U}$ et $\vec{V}$ soient colinéaires: 2) Déterminer la valeur de y potur que les vecteurs $\vec{p}$ et $\vec{Q}$ soient perpendiculaires:

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Problem 262

Soient les vecteurs: $\vec{U}=2 \vec{i}+6 \vec{k}, \vec{V}=8 \vec{i}+y \vec{j}+z \vec{k}, \vec{P}=3 \vec{i}-4 \vec{j}+2 \vec{k}, \vec{Q}=-2 \vec{i}+y \vec{j}+12 \vec{k}$ 1) Déterminer yet $z$ pour que les vecteurs $\vec{U}$ et $\vec{V}$ soient colinéaires: 2) Déterminer la valeur de y potur que les vecteurs $\vec{p}$ et $\vec{Q}$ soient perpendiculaires:

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Problem 263

In the coordinate plane, the point $A(-2,2)$ is translated to the point $A^{\prime}(0,3)$ . Under the same translation, the points $B(1,5)$ and $C(-5,0)$ are translated to $B^{\prime}$ and $C^{\prime}$ , respectively. What are the coordinates of $B^{\prime}$ and $C^{\prime}$ ? B. (1) c.(1)

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Problem 264

3. $\triangle D E F$ has vertices at $D(8,-2), E(1,-3)$ , and $F(9,-9)$ . Use special segments to determine if $E F$ is the base of an isosceles triangle. $\rho(8,-2)$

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Problem 265

Runde 1 1 a) Bestimmen sie eine Parameter- und eine Koordinatengleichung der Ebene, in der di Punkie $A(2|5| 1), B(0|-1| 3)$ und $C(7|2| 5)$ liegen. b) Untersuchen Sie, ob der Punkt $P(4|4|-3)$ in der Ebene $E: x_{1}-x_{2}+2 x_{3}=5 \mathrm{bzW}$ . in cler Eberse $F: \vec{x}=\left(\begin{array}{r}1 \\ 0 \\ -1\end{array}\right)+r \cdot\left(\begin{array}{l}4 \\ 2 \\ 1\end{array}\right)+s \cdot\left(\begin{array}{r}1 \\ -2 \\ 3\end{array}\right)$ liegt.

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Problem 266

Find the product, $A B$ , of the two complex numbers.

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Problem 267

A 100 -pound weight is to be dragged up a $20^{\circ}$ ramp. We want to know how hard to pull on the cable to move the weight up the ramp (if friction is ignored). That is, we need to know the magnitude of the component of the weight vector in the direction opposite the cable. How hard do we need to pull on the cable?

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Problem 268

a) $(-5 \vec{\imath}-2 \vec{\jmath})+(3 \vec{\imath}+6 \vec{\jmath})$ $-2 \vec{\imath}+4 \vec{\jmath} \quad$ Same as $\langle-2,4\rangle$

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Problem 269

5. Forces of 15 N and 11 N act a point at $125^{\circ}$ to each other. Find the magnitude of the resultant.

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Problem 270

1. $(\vec{i} \times \vec{j}) \cdot \vec{k}=\vec{i} \cdot(\vec{j} \times \vec{k})$ .
2. If $\vec{v}$ and $\vec{w}$ are any two vectors, then $\|\vec{v}+\vec{w}\|=\|\vec{v}\|+\|\vec{w}\|$ .
3. The value of $\vec{v} \cdot(\vec{v} \times \vec{w})$ is always zero.
4. For any scalar $c$ and any vector $\vec{v}$ , we have $\|c \vec{v}\|=c\|\vec{v}\|$ . earn $50 \%$ partial credit for 2 - 3 correct answers. Answers Submit Answers npted this problem 2 times. corded score is $0 \%$ . empts remainina.

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Problem 271

If $\mathbf{a}=\mathbf{i}+\mathbf{j}+3 \mathbf{k}$ and $\mathbf{b}=\mathbf{i}+\mathbf{j}+3 \mathbf{k}$ Compute the cross product $\mathbf{a} \times \mathbf{b}$ . $\mathbf{a} \times \mathbf{b}=\square \mathrm{i}+\square \mathrm{j}+\square \mathrm{k}$

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Problem 272

Find the midpoint of the line segment with the given endpoints. $(2,8) \text { and }(4,6)$
The midpoint of the segment is . $\square$ (Type an ordered pair.)

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Problem 273

Find $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3 \mathbf{v}$ for $u=\begin{bmatrix}-3 \\ 6\end{bmatrix}, v=\begin{bmatrix}-5 \\ 4\end{bmatrix}$ .

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Problem 274

Find $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3 \mathbf{v}$ for $u=\begin{bmatrix}-3 \\ 6\end{bmatrix}$ and $v=\begin{bmatrix}-5 \\ 4\end{bmatrix}$ .

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Problem 275

Is vector $b$ a linear combination of $a_{1}, a_{2}, a_{3}$ ? Choose A, B, C, or D based on the echelon matrix pivots.

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Problem 276

Describe the Span $\{\mathbf{v}_{1}, \mathbf{v}_{2}\}$ for $\mathbf{v}_{1}=\begin{bmatrix}4 \\ 10 \\ -2\end{bmatrix}$ and $\mathbf{v}_{2}=\begin{bmatrix}10 \\ 25 \\ -5\end{bmatrix}$ . Choose A, B, C, or D.

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Problem 277

Find the value(s) of $h$ so that the vector $b = \left[\begin{array}{r}4 \\ -9 \\ h\end{array}\right]$ lies in the plane spanned by $a_{1} = \left[\begin{array}{r}1 \\ 3 \\ -1\end{array}\right]$ and $a_{2} = \left[\begin{array}{r}-6 \\ -11 \\ 2\end{array}\right]$ . The value(s) of $h$ is(are) $\square$ .

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Problem 278

Do the vectors $\mathbf{v}_{1} = \begin{bmatrix} 0 \\ 0 \\ -3 \end{bmatrix}$ , $\mathbf{v}_{2} = \begin{bmatrix} 0 \\ -5 \\ 6 \end{bmatrix}$ , and $\mathbf{v}_{3} = \begin{bmatrix} 5 \\ -3 \\ 9 \end{bmatrix}$ span $\mathbb{R}^{3$? Explain.

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Problem 279

Find the vectors $\overrightarrow{P Q}$ and $\overrightarrow{P R}$ for points $P(-2,1)$ , $Q(5,3)$ , and $R(x,y)$ .

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Problem 280

Find the midpoint of the line segment joining the points $R(-2,3)$ and $S(4,6)$ .
The midpoint is $\square$ (Type an ordered pair. Use integers or simplified fractions for any numbers in the expression.)

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Problem 281

2 Quadrilateral QRST is transformed by the rule $(x, y) \rightarrow(-x, y)$ to create quadrilateral $Q^{\prime} R^{\prime} S^{\prime} T^{\prime}$ . a) How are the corresponding side lengths affected by the transformation?
The Corresponaling b) How are the corresponding angles affected by the transformation? $\qquad$ continue $\qquad$ d) How is the area of the quadrilateral affected? e) How is the perimeter of the quadrilateral affected?

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Problem 282

2 Quadrilateral QRST is transformed by the rule $(x, y) \rightarrow(-x, y)$ a) How are the corresponding side lengths affected by the transformation?
The Corresponaling b) How are the corresponding angles affected by the transformation? $\qquad$ De c) How is the orientation of the quadrilateral affected? $\qquad$ reversed d) How is the area of the quadrilateral affected? e) How is the perimeter of the quadrilateral affected?

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Problem 283

Let $\mathbf{v}_{1}=\left[\begin{array}{r}1 \\ 0 \\ -1\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{l}4 \\ 1 \\ 5\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{r}7 \\ 2 \\ 11\end{array}\right]$ , and $\mathbf{w}=\left[\begin{array}{l}5 \\ 1 \\ 4\end{array}\right]$ . a. Is $\mathbf{w}$ in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? How many vectors are in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? b. How many vectors are in $\operatorname{Span}\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? c. Is $\mathbf{w}$ in the subspace spanned by $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? Why? a. Is $\mathbf{w}$ in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? A. Vector $\mathbf{w}$ is not in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ because it is not a linear combination of $\mathbf{v}_{1}, \mathbf{v}_{2}$ , and $\mathbf{v}_{3}$ . B. Vector $\mathbf{w}$ is in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ because the subspace generated by $\mathbf{v}_{1}, \mathbf{v}_{2}$ , and $\mathbf{v}_{3}$ is $\mathbb{R}^{3}$ . C. Vector $\mathbf{w}$ is not in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ because it is not $\mathbf{v}_{1}, \mathbf{v}_{2}$ , or $\mathbf{v}_{3}$ . D. Vector $\mathbf{w}$ is in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ because it is a linear combination of $\mathbf{v}_{1}, \mathbf{v}_{2}$ , and $\mathbf{v}_{3}$ .
How many vectors are in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The number of vectors in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ is $\square$ . B. There are infinitely many vectors in $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ . b. How many vectors are in $\operatorname{Span}\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The number of vectors in $\operatorname{Span}\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ is $\square$ $\square$ . B. There are infinitely many vectors in Span $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ .

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Problem 284

When plotting the resultant from three or more vectors, it is most convenient to use the $\qquad$ method. (A) parallelogram (B) head-to-tail (C) histogram (D) bar chart

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Problem 285

Find the polar coordinates, $0 \leq \theta<2 \pi$ and $r \geq 0$ , of the point given in Cartesian coordinates. A) $\left(2, \frac{5 \pi}{4}\right)$ B) $\left(2, \frac{7 \pi}{4}\right)$ $(\sqrt{2},-\sqrt{2})$ C) $\left(\sqrt{2}, \frac{7 \pi}{4}\right)$ D) $\left(4, \frac{5 \pi}{4}\right)$

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Problem 286

3. Two horizontal forces act on a $5.0-\mathrm{kg}$ mass. One force has a magnitude of 8.0 N and is directed due north. The second force toward the east has a magnitude of 6.0 N . What is the acceleration of the mass? A) $1.6 \mathrm{~m} / \mathrm{s}^{2}$ due north B) $1.2 \mathrm{~m} / \mathrm{s}^{2}$ due east C) $2.0 \mathrm{~m} / \mathrm{s}^{2}$ at 53 e N of E
ㅇ) $2.0 \mathrm{~m} / \mathrm{s}^{2}$ at $53 \mathrm{~m} E$ of N

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Problem 287

Find $<3 \bar{u}, 4 \bar{v}+5 \bar{w}>$ , given that $\langle\bar{u}, \bar{v}>=6,<\bar{v}, \bar{w}>=-5$ , and $<\bar{u}, \bar{w}>=-1$ Number

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Problem 288

1 Forces
19. Two ropes are attached to a tree, and forces of $\vec{F}_{1}=2.0 \hat{i}+4.0 \hat{j} \mathrm{~N}$ and $\vec{F}_{2}=3.0 \hat{i}+6.0 \hat{j} \mathrm{~N}$ are applied. The forces are coplanar (in the same plane). (a) What is the resultant (net force) of these two force vectors? (b) Find the magnitude and direction of this net force.

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Problem 289

20. A telephone pole has three cables pulling as shown from above, with $\vec{F}_{1}=(300.0 \hat{i}+500.0 \hat{j}), \vec{F}_{2}=-200.0 \hat{i}$ , and $\vec{F}_{3}=-800.0 \hat{j}$ . (a) Find the net force on the telephone pole in component form. (b) Find the magnitude and direction of this net force.

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Problem 290

1. Two teenagers are pulling on ropes attached to a tree. The angle between the ropes is $30.0^{\circ}$ . David pulls with a force of 400.0 N and Stephanie pulls with a force of 300.0 N . (a) Find the component form of the net force. (b) Find the magnitude of the resultant (net) force on the tree and the angle it makes with David's rope.

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Problem 291

with David's rope. 5.2 Newton's First Law
22. Two forces of $\vec{F}_{1}=75.02(\hat{i}-\hat{j}) \mathrm{N}$ and $\vec{F}_{2}=\frac{150.0}{\sqrt{2}}(\hat{i}-\hat{j}) \mathrm{N}$ act on an object. Find the third force $\vec{F}_{3}$ that is needed to balance the first two forces.

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Problem 292

23. While sliding a couch across a floor, Andrea and Jennifer exert forces $\vec{F}_{A}$ and $\vec{F}_{J}$ on the couch. Andrea's force is due north with a magnitude of 130.0 N and Jennifer's force is $32^{\circ}$ east of north with a magnitude of 180.0 N . (a) Find the net force in component form. (b) Find the magnitude and direction of the net force. (c) If Andrea and Jennifer's housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force $\vec{F}_{D S}$ should they push so that the couch does not move?

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Problem 293

38. Suppose that the particle of the previous problem also experiences forces $\vec{F}_{2}=-15 \hat{i} \mathrm{~N}$ and $\vec{F}_{3}=6.0 \hat{j} \mathrm{~N}$ . What is its acceleration in this
39. Find the acceleration of the body of mass 5.0 kg shown below.

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Problem 294

39. Find the acceleration of the body of mass 5.0 kg shown below.

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Problem 295

40. In the following figure, the horizontal surface on which this block slides is frictionless. If the two forces acting on it each have magnitude $F=30.0 \mathrm{~N}$ and M $=10.0 \mathrm{~kg}$ , what is the magnitude of the resulting acceleration of the block?

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Problem 296

Two muscles in the back of the leg pull upward on the Achilles tendon, as shown below. (These muscles are called the medial and lateral heads of the gastrocnemius muscle.) Find the magnitude and direction of the total force on the Achilles tendon. What type of movement could be caused by this force?

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Problem 297

Question 4 (1 point) How will this object move? a It won't move. b It will move to the left. c It will move to the right. d It will move up.

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Problem 298

Question 7 (1 point) What is the net force in this diagram? a $\quad 8 \mathrm{~N}$ right b $\quad 5 \mathrm{~N}$ right c 2 N right d 2 Nleft

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Problem 299

Find a subset of the following set of vectors that forms a basis for the span(S). $(1,0,-2,3),(0,1,2,3),(2,-2,-8,0),(2,-1,10,3),(3,-1,-6,9)$

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Problem 300

$2 A B C D$ is a rhombus of center $O$ , having a side of 4 cm and such that $\hat{A}=60^{\circ}$ . $I, J, K$ and $L$ are the midpoints of $[A D],[A B]$ , $[B C]$ and $[C D]$ respectively. $1^{\circ}$ Replace the symbol * by a point from the figure : a) $\overrightarrow{A I}=\overrightarrow{K^{}}$ b) $\vec{C} =\overrightarrow{K O}$ c) $\overrightarrow{W_{D}}=\overrightarrow{J O}$ d) $\vec{O} L=\vec{J}$ e) $\overrightarrow{K B}=\overrightarrow{B I}$ f) $\overrightarrow{O D}=\overrightarrow{B }$ $2^{\circ}$ Name the vectors equal to $\overrightarrow{I J}$ and equal to $\overrightarrow{A I}$ . $3^{\circ}$ Construct vector $\overrightarrow{A R}=\overrightarrow{D B}$ and vector $\overrightarrow{B P}=\overrightarrow{D A}$ . What do you notice ? $4^{\circ}$ Answer by True or False. a) $\overrightarrow{A I}=\overrightarrow{A J}$ b) $\overrightarrow{D L}=\overrightarrow{B K}$ folse c) $\overrightarrow{I J}=\overrightarrow{L K}$ Tfue d) $\overrightarrow{A R}=\overrightarrow{C D}$ falsc e) $\overrightarrow{A B}=-\overrightarrow{C B}$ f) $\overrightarrow{A D}=-\overrightarrow{C B}$ True g) $\overrightarrow{B I}=\overrightarrow{K D}$ . True $5^{\circ}$ Complete by $=$ or $\neq$ a) $\|\overrightarrow{A D}\| \ldots\|\overrightarrow{C D}\|$ b) $\overrightarrow{\mathrm{BC}}=\overrightarrow{\mathrm{AD}}$ c) $\overrightarrow{I J} \leftrightarrows \overrightarrow{K L}$ d) $\overrightarrow{B J} \therefore \overrightarrow{L D}$ e) $\|\overrightarrow{I K}\| \ldots\|\overrightarrow{J L}\|-\operatorname{mag} i t$ ade f) $\overrightarrow{O I} . \ldots \overrightarrow{O K}$ g) $\overrightarrow{L O} \doteqdot \overrightarrow{O J}$ h) $\overrightarrow{C K}=\overrightarrow{I A}$ . $6^{\circ}$ Complete by the convenient vector : a) The opposite of $\overrightarrow{B C}$ is $C R$ b) Vectors $\overrightarrow{A J}$ and ......... are equal. c) Vectors $\overrightarrow{L D}$ and $J R$ . are opposite. $\qquad$ d) The opposite of vector $\overrightarrow{A B}+\overrightarrow{C D}$ is $7^{\circ}$ Write $\overrightarrow{A B}$ as a sum of three vectors, then of four vectors. $8^{\circ}$ Calculate : a) $\|\overrightarrow{A I}+\overrightarrow{I B}\|$ b) $\|\overrightarrow{A D}+\overrightarrow{O J}\|$ c) $\|\overrightarrow{A O}+\overrightarrow{B J}\|$ d) $\|\overrightarrow{A D}+\overrightarrow{C B}\|$ .

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Vector

Problem 201

Sketch the figure for XY¨⊥YZundefined\ddot{XY} \perp \overrightarrow{YZ}XY¨⊥YZ. What’s the first step: A, B, C, or D?

Problem 202

Find point BBB on line segment AC‾\overline{AC}AC such that the ratio AB:AC=1:3AB : AC = 1 : 3AB:AC=1:3 where A=(−2,4)A=(-2,4)A=(−2,4) and C=(4,7)C=(4,7)C=(4,7).

Problem 203

Problem 204

Problem 205

Problem 206

Problem 207

Problem 208

Problem 209

What is angle for the point M(−1,0)M(-1,0)M(−1,0) ?A 270 B -90C 90 D 180SUBMIT ANSWER

Problem 210

arx Maths 1 A 18 1c1 c1c 1D 1E1 E1E Summary Bookwork code: IA Calculator not allowedWhat are the coordinates of the point halfway between the origin and point AAA on the coordin Zoom

Problem 211

Problem 212

Problem 213

Problem 214

Problem 215

Problem 216

Problem 217

Problem 218

Find the pre-image of vertex A′(8,5)A^{\prime}(8,5)A′(8,5) after reflection across the yyy-axis. Options: (−8,−6)(-8,-6)(−8,−6), (−6,8)(-6,8)(−6,8), (8,6)(8,6)(8,6), (6,−8)(6,-8)(6,−8).

Problem 219

Find which reflection of the segment from (−4,−6)(-4,-6)(−4,−6) to (−6,4)(-6,4)(−6,4) gives endpoints (4,−6)(4,-6)(4,−6) and (6,4)(6,4)(6,4).

Problem 220

Problem 221

Find the midpoint of the line segment with endpoints K(7,7)K(7,7)K(7,7) and L(1,3)L(1,3)L(1,3). Choose from the options: A. (−3,−2)(-3,-2)(−3,−2) B. (3,−2)(3,-2)(3,−2) C. (−3,2)(-3,2)(−3,2) D. (3,2)(3,2)(3,2).

Problem 222

Problem 223

Problem 224

Problem 225

Problem 226

Problem 227

Найди координаты вершины N параллелограмма MNKL, если M(−3;−1),K(5;4)\mathrm{M}(-3 ;-1), \mathrm{K}(5 ; 4)M(−3;−1),K(5;4) и L(2;−1)\mathrm{L}(2 ;-1)L(2;−1).Запиши числа в поля ответа. □\square□ □\square□ )

Problem 228

Problem 229

Give a vector parametric equation for the line through the point (−1,0,4)(-1,0,4)(−1,0,4) that is parallel to the line ⟨4−5t,4−4t,5−2t⟩\langle 4-5 t, 4-4 t, 5-2 t\rangle⟨4−5t,4−4t,5−2t⟩ : L(t)=L(t)=L(t)=

Problem 230

Problem 231

Problem 232

Si u⃗=[3,4]\vec{u}=[3,4]u=[3,4] et v⃗=[6,k]\vec{v}=[6, k]v=[6,k], quelle est la valeur de kkk si les deux vecteurs sont orthogonaux.

Problem 233

Find the midpoint of the segment with endpoints (−2,3)(-2,3)(−2,3) and (5,−3)(5,-3)(5,−3).

Problem 234

Identify the opposite ray to NMundefined\overrightarrow{N M}NM from the options: NOundefined\overrightarrow{N O}NO, MMM, NPundefined\overrightarrow{N P}NP, MPundefined\overrightarrow{M P}MP, or all of the above.

Problem 235

Find the midpoint of the segment with endpoints (−9,−2)(-9,-2)(−9,−2) and (−1,−8)(-1,-8)(−1,−8).

Problem 236

Find the coordinates that divide the line segment from (2,−6)(2,-6)(2,−6) to (5,6)(5,6)(5,6) in a 1:5 ratio.

Problem 237

Problem 238

Problem 239

Problem 240

Problem 241

Problem 242

Problem 243

1 pointGiven pˉ=2x+1x2\bar{p}=2 x+1 x^{2}pˉ​=2x+1x2, find the norm of ppp

Problem 244

- Question 31 point Number HelpFind <5uˉ,5vˉ+2wˉ><5 \bar{u}, 5 \bar{v}+2 \bar{w}><5uˉ,5vˉ+2wˉ>, given that <uˉ,vˉ>=4,<vˉ,wˉ>=−5<\bar{u}, \bar{v}>=4,<\bar{v}, \bar{w}>=-5<uˉ,vˉ>=4,<vˉ,wˉ>=−5, and <uˉ,wˉ>=−2<\bar{u}, \bar{w}>=-2<uˉ,wˉ>=−2 Number

Problem 245

Problem 246

Problem 247

Problem 248

Find the area of the parallelogram with vertices at (-4,-5), (3,-3), (-4,-9), (3,-7).

Problem 249

Problem 250

Find the midpoint of the line segment with the given endpoints. (−6,−3) and (−1,−5)(-6,-3) \text { and }(-1,-5)(−6,−3) and (−1,−5)The midpoint is □\square□ (Type an ordered pair.)

Problem 251

Problem 252

Problem 253

Problem 254

Problem 255

Graph the reflection of the point T(10,−2)T(10,-2)T(10,−2) over the xxx-axis.

Problem 256

Reflect the point S(0,2)S(0,2)S(0,2) over the xxx-axis. What are the coordinates of S′S^{\prime}S′?

Problem 257

Exercice 01 : Detx points AAA et BBB, ont pour coordonnées cartésiennes dans l'espace : A(2,3,−3),B(5,7,2)A(2,3,-3), B(5,7,2)A(2,3,−3),B(5,7,2) Déterminer les composantes du vecteur ABundefined\overrightarrow{A B}AB ainsi que son module, sa direction et son sens.

Problem 258

Sketch the figure for $\ddot{XY} \perp \overrightarrow{YZ}$ . What’s the first step: A, B, C, or D?

Find point $B$ on line segment $\overline{AC}$ such that the ratio $AB : AC = 1 : 3$ where $A=(-2,4)$ and $C=(4,7)$ .

What is angle for the point $M(-1,0)$ ?
A 270 B -90
C 90 D 180
SUBMIT ANSWER

arx Maths 1 A 18 $1 c$ 1D $1 E$ Summary Bookwork code: IA Calculator not allowed
What are the coordinates of the point halfway between the origin and point $A$ on the coordin Zoom

Find the pre-image of vertex $A^{\prime}(8,5)$ after reflection across the $y$ -axis. Options: $(-8,-6)$ , $(-6,8)$ , $(8,6)$ , $(6,-8)$ .

Find which reflection of the segment from $(-4,-6)$ to $(-6,4)$ gives endpoints $(4,-6)$ and $(6,4)$ .

Find the midpoint of the line segment with endpoints $K(7,7)$ and $L(1,3)$ . Choose from the options: A. $(-3,-2)$ B. $(3,-2)$ C. $(-3,2)$ D. $(3,2)$ .

Найди координаты вершины N параллелограмма MNKL, если $\mathrm{M}(-3 ;-1), \mathrm{K}(5 ; 4)$ и $\mathrm{L}(2 ;-1)$ .
Запиши числа в поля ответа. $\square$ $\square$ )

Give a vector parametric equation for the line through the point $(-1,0,4)$ that is parallel to the line $\langle 4-5 t, 4-4 t, 5-2 t\rangle$ : $L(t)=$

Si $\vec{u}=[3,4]$ et $\vec{v}=[6, k]$ , quelle est la valeur de $k$ si les deux vecteurs sont orthogonaux.

Find the midpoint of the segment with endpoints $(-2,3)$ and $(5,-3)$ .

Identify the opposite ray to $\overrightarrow{N M}$ from the options: $\overrightarrow{N O}$ , $M$ , $\overrightarrow{N P}$ , $\overrightarrow{M P}$ , or all of the above.

Find the midpoint of the segment with endpoints $(-9,-2)$ and $(-1,-8)$ .

Find the coordinates that divide the line segment from $(2,-6)$ to $(5,6)$ in a 1:5 ratio.

1 point
Given $\bar{p}=2 x+1 x^{2}$ , find the norm of $p$

- Question 3
1 point Number Help
Find $<5 \bar{u}, 5 \bar{v}+2 \bar{w}>$ , given that $<\bar{u}, \bar{v}>=4,<\bar{v}, \bar{w}>=-5$ , and $<\bar{u}, \bar{w}>=-2$ Number

Find the midpoint of the line segment with the given endpoints. $(-6,-3) \text { and }(-1,-5)$
The midpoint is $\square$ (Type an ordered pair.)

Graph the reflection of the point $T(10,-2)$ over the $x$ -axis.

Reflect the point $S(0,2)$ over the $x$ -axis. What are the coordinates of $S^{\prime}$ ?

Exercice 01 : Detx points $A$ et $B$ , ont pour coordonnées cartésiennes dans l'espace : $A(2,3,-3), B(5,7,2)$ Déterminer les composantes du vecteur $\overrightarrow{A B}$ ainsi que son module, sa direction et son sens.

Exercice 01 : Detx points $A$ et $B$ , ont pour coordonnées cartésiennes dans l'espace : $A(2,3,-3), B(5,7,2)$ Déterminer les composantes du vecteur $\overrightarrow{A B}$ ainsi que son module, sa direction et son sens.

Exercice 02 : La résultante de deux forces $\vec{F}_{1}$ et $\vec{F}_{2}$ est égale à 50 N et fait un angle de $30^{\circ}$ avec la force $F_{1}=15 \mathrm{~N}$ . Trouver le module de la force $\vec{F}_{2}$ et l'angle entre les deux forces.

3. $\triangle D E F$ has vertices at $D(8,-2), E(1,-3)$ , and $F(9,-9)$ . Use special segments to determine if $E F$ is the base of an isosceles triangle. $\rho(8,-2)$

Find the product, $A B$ , of the two complex numbers.

a) $(-5 \vec{\imath}-2 \vec{\jmath})+(3 \vec{\imath}+6 \vec{\jmath})$ $-2 \vec{\imath}+4 \vec{\jmath} \quad$ Same as $\langle-2,4\rangle$

5. Forces of 15 N and 11 N act a point at $125^{\circ}$ to each other. Find the magnitude of the resultant.

Find the midpoint of the line segment with the given endpoints. $(2,8) \text { and }(4,6)$
The midpoint of the segment is . $\square$ (Type an ordered pair.)

Find $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3 \mathbf{v}$ for $u=\begin{bmatrix}-3 \\ 6\end{bmatrix}, v=\begin{bmatrix}-5 \\ 4\end{bmatrix}$ .

Find $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3 \mathbf{v}$ for $u=\begin{bmatrix}-3 \\ 6\end{bmatrix}$ and $v=\begin{bmatrix}-5 \\ 4\end{bmatrix}$ .