Not sure if I should be in this thread or in the geometry one, but here goes:

The problem that I was given was:

Find the area of a paralellogram spanned by the vectors a = i + j and b = 4i - j

Now prove the following |a X b| =|a||b|sin(theta) for ANY ( 2 dimensional ) vectors a and b where theta is the angle between the vectors.

Now I know that the area of a parrallogram is the magnitude of the cross product, and I can easily show that the area of the parrallelogram is the same as |a||b|sin(theta), but how do you prove that |axb| = area of parrelelogram?