Magnitude of Cross Product Mismatch

[4570562]

Homework Statement

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

Homework Equations

||w x u|| = ||w|| ||u|| sin θ


cos θ = \frac{w.u}{||w|| ||u||}

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?

 

[Dick]

Homework Statement

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

Homework Equations

||w x u|| = ||w|| ||u|| sin θ


cos θ = \frac{w.u}{||w|| ||u||}

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?

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

 

[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.