Simple vector cross product question.

Question

How do you compute the cross product of two vectors in the following form:

$r_{u} = \cos(\theta)\textbf{x} + \sin(\theta)\textbf{y}$

$r_{v} = -\cos(\theta)\textbf{x} - \sin(\theta)\textbf{y}$

I have completely forgotten. This is just an example I created off the top of my head.

Answer 1

They are parallel ($r_u=-r_v$) so the cross product is by the property of antisymmetry equal to zero.