Math  /  Algebra

Question11. Three vectors are given by P=3i3j2K^,Qiji+2 K\vec{P}=3 i-3 j-2 \hat{K}, \vec{Q}-i-j i+2 \mathrm{~K} and S=2i+2j+K\vec{S}=2 \mathrm{i}+2 \mathrm{j}+\mathrm{K}. Then get 2P(3Q+S)?6i6j4k(3i+12j+6k+2i+2j+k)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 C\vec{C} lying along +y-axis does A(QC)=0\vec{A} \cdot(\vec{Q}-\vec{C})=0 given that A3i2j+k\vec{A}-3 i-2 j+k and B=4i+5j+7k\vec{B}=4 i+5 j+7 k ? ) (i10j+7k)(-i-10 j+7 k)
13. Given that P=5i6j,Q=2i+3j\vec{P}=5 i-6 \mathrm{j}, \vec{Q}=-2 i+3 \mathrm{j} and R\vec{R} lies in the xy plane perpendicular to P\vec{P} 15 If the dot product of R\vec{R} and Q\vec{Q} is 9 . Then get R\vec{R} ? RQ=undefined=RxQx+RyQy\vec{R} \vec{Q} \overrightarrow{=}=R_{x} Q_{x}+R_{y} Q_{y}
14. Find R=ai+bj+k\vec{R}=\mathrm{a} i+\mathrm{bj}+\mathrm{k} which is perpendicular to both A=3i+jK\vec{A}=3 i+j-\mathrm{K} and +3Ry+3 R_{y} B=3i+2j+2k\vec{B}=-3 i+2 j+2 k. 5Rx6Ry=04i1/3d5 R_{x}-6 R_{y}=0 \quad 4 i-1 / 3 d
15. Let A=i+j+K^\vec{A}=i+j+\hat{K} and B=2i+2j+2k\vec{B}=2 i+2 j+2 \mathrm{k} what is the angle between A\vec{A} and B\vec{B} ?
16. Find a such that, the angle between A=i+aj\vec{A}=i+a j and B=i+j\vec{B}=i+j is 4545^{\circ}. ( sin45=\sin 45^{\circ}= cos45=12)\left.\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right) it 2\sqrt{2} B=αi3j+5kα\vec{B}=\stackrel{\alpha}{\alpha i-3 \propto j+5 k} orthogonal
17. For what value of \propto are the vectors A=αi2j+k^\vec{A}=\alpha i-2 j+\hat{k} and B=ai3j+5\vec{B}=a i-3 \propto j+5 to each other? α=1\quad \alpha=-1 or α=5i2j+ki+3j+5\alpha=-5-i-2 j+k \quad-i+3 j+5
18. Consider a block placed on a horizontal surface and that force F\vec{F} is applied on the block to move the block through displacement S\vec{S}. If F=(5i+3j)N\vec{F}=(5 i+3 j) N and s=(2i+4j)m\vec{s}=(-2 i+4 j) \mathrm{m} then calculate the work done? 5i2j+k5i+1sj+5\quad-5 i-2 j+k \quad 5 i+1 s j+5 19.Vector A\vec{A} has a magnitude of 6 units along the positve x2530x-25-30, Vector B\vec{B} has amagnitude of 4 units and lies on xy-plane making an angle of 6060^{\circ} with the positive x -axis. What is the scalardot product of A\vec{A} and B\vec{B} ? 20. i.If AB=AB\vec{A} \cdot \vec{B}=|A||B|, what can you say about vector A\vec{A} and B\vec{B} ? ii. if P+Q=O\vec{P}+\vec{Q}=O, then tell about vectors P\vec{P} and Q\vec{Q} ? iii. use the given diagram and express N,M\vec{N}, \vec{M} and Z\vec{Z} interns of Q\vec{Q} ? 36+3Ry=9Ry=1518i+15y=18(α+1)(α+5)α2+6α+5\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}

Studdy Solution
Multiply the resulting vector by 27.
27.(3Q+S)=27(2i10j+7k) 27.(3Q + S) = 27(2i - 10j + 7k) =54i270j+189k = 54i - 270j + 189k
The result for problem 11 is 54i270j+189k 54i - 270j + 189k .

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