Question

Someone draw a picture of what cross producting does

Answer 1

It also produces a vector normal to the plane that a and b are in.

Answer 2

I'm grabbing most of this from wikipedia lolol.
My understanding of vectors has slipped away a little bit XD

Answer 3

The cross-product of two vectors is a vector.
So in that first picture I should have a bit more clear.
The magnitude of that resulting vector would be the area.

Answer 4

Indeed, it would produce a vector perpendicular to the parallelogram spanned by the two vectors, with magnitude of the area of that parallelogram.