Question

prove that cross product of two vectors is equal to the area of a parallelogram

Answer 1

Let A and B be two vectors.
A × B = |A| |B| sin(Ф)    where
     |A| = magnitude of A
     |B| = magnitude of B
     Ф = angle between A and B
If you draw a parallelogram with sides as vector A and B
The area of the parallelogram will be |B|h as shown in figure.
But h = |A| sin(Ф)
So area = |B|h = |A| |B| sin(Ф) = A × B