# Homework Help: Magnitude of Cross Product Mismatch

1. Jan 20, 2012

### 4570562

1. The problem statement, all variables and given/known data

Find the magnitude of the vector product w ⃗x u, where w=<1,0,1> and u=<1,1,0>.

2. Relevant equations

||w x u|| = ||w|| ||u|| sin θ

cos θ = $\frac{w.u}{||w|| ||u||}$

3. The attempt at a solution
w ⃗x u ⃗= -i ̂+j ̂+k ̂
‖||w ⃗x u|| ⃗ ‖= √3

but

cos⁡θ= (w ⃗∙ u ⃗)/(‖||w|| ⃗||u||) ⃗ ‖ = 1/(√2 √2) implying ⟹ θ=$\pi$/4
which then makes
‖||w ⃗x u|| ⃗ ‖= ‖||w|| ⃗||‖‖u|| ⃗sin⁡θ
become
‖||w ⃗x u|| ⃗ ‖= √2 √2 sin⁡〖$\pi$/4
or the sqrt(2).

What's wrong here?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 20, 2012

### Dick

You've got cos(theta)=1/2. That doesn't show theta=pi/4. It's not. What is it?

3. Jan 20, 2012

### 4570562

Thank you so much.
cos theta = .5 implies that theta is pi/3 , which would make it work both ways. I can't tell you how long I have been just staring at this problem. Thanks.