# Finding Magnitude of Vector

1. Jan 28, 2012

### Rapier

1. The problem statement, all variables and given/known data
Let u = <3,-1>. Find v such that ||v||=4 and the angle between the vectors is ∏/3.

2. Relevant equations

u.v = ||u|| ||v|| cos θ

3. The attempt at a solution

<3,-1>.v = (√10)(4) cos ∏/3
<3,-1>.v = 2√10
v = <(2√10)/3, (2√10)/-1>

Can you please confirm that I am doing this correctly, or if not help me through where I am going awry?

2. Jan 28, 2012

### SammyS

Staff Emeritus
You're not doing this correctly. The v you have has a magnitude that's way too big.

Write vector, v, as v = <vx, vy>, where vx2 + vy2 = 16 .
Solve this for vy.​

<3,-1>∙v = (√10)(4) cos ∏/3

<3,-1>∙v = 2√10​
are fine.

But in the next line, it looks like you tried to divide by the vector <3,-1>. There is no such thing as vector division !

Compute <3,-1>∙v = (3)vx + (-1)vy.

Of course that gives you: (3)vx + (-1)vy = 2√(10)

Solve that equation and the equation, vx2 + vy2 = 16, simultaneously.