Anyone have an easy way for computing cross-products? I came across:

a x b = A_(x)b = [[0, -a_3, a_2],[a_3, 0, -a_1],[-a_2, a_1, 0]] multiplied with vector [b_1, b_2, b_3].

which seems very useful.

My book attempts to solve it by using determinants;

Also, if we have two vectors, a and b, in R^2, is a x b defined?

I've only seen this done with vectors in R^3.

Lastly, if we have two vectors a and b, I'm assuming those vectors are related to the a x b where their product is = 0, thus they're orthogonal?

Thanks.