[Math] finding out if two vectors are perpendicular or parallel

Question

I'm not sure if I quite get this. For example,

(1, -1) and (-3, 3)

take the cross product, you will end up with
-3 + (-3)

This doesn't equal 0, so it's not perpendicular. So that leaves me with it being parallel. When are two vectors parallel?

Answer 1

Two vectors $v_1=(x_1,y_1)$ and $v_2=(x_2,y_2)$ are parallel iff $x_1 \, y_2 = x_2 \, y_1$.