Studdy AI Logo
Math  /  Geometry

Question2. What is the magnitude of resultant vector where u⃗=⟨−42,−2⟩ and v⃗=⟨52,3⟩\vec{u}=\langle-4 \sqrt{2},-2\rangle \text { and } \vec{v}=\langle 5 \sqrt{2}, 3\rangle

Studdy Solution

STEP 1

1. The vectors u⃗\vec{u} and v⃗\vec{v} are given in component form.
2. The magnitude of the resultant vector r⃗\vec{r} is calculated as r⃗=u⃗+v⃗\vec{r} = \vec{u} + \vec{v}.

STEP 2

1. Find the resultant vector by adding the components of u⃗\vec{u} and v⃗\vec{v}.
2. Calculate the magnitude of the resultant vector.

STEP 3

Find the resultant vector r⃗\vec{r} by adding the components of u⃗\vec{u} and v⃗\vec{v}:
r⃗=u⃗+v⃗=⟨−42,−2⟩+⟨52,3⟩\vec{r} = \vec{u} + \vec{v} = \langle -4\sqrt{2}, -2 \rangle + \langle 5\sqrt{2}, 3 \rangle
Calculate each component:
r⃗=⟨(−42+52),(−2+3)⟩\vec{r} = \langle (-4\sqrt{2} + 5\sqrt{2}), (-2 + 3) \rangle
r⃗=⟨2,1⟩\vec{r} = \langle \sqrt{2}, 1 \rangle

STEP 4

Calculate the magnitude of the resultant vector r⃗\vec{r}:
The formula for the magnitude of a vector ⟨a,b⟩\langle a, b \rangle is:
∣r⃗∣=a2+b2|\vec{r}| = \sqrt{a^2 + b^2}
Substitute the components of r⃗\vec{r}:
∣r⃗∣=(2)2+(1)2|\vec{r}| = \sqrt{(\sqrt{2})^2 + (1)^2}
∣r⃗∣=2+1|\vec{r}| = \sqrt{2 + 1}
∣r⃗∣=3|\vec{r}| = \sqrt{3}
The magnitude of the resultant vector is:
3 \boxed{\sqrt{3}}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord