Cross product and the angles of a prallelogram

[rado5]

Cross product and the angles of a prallelogram's diameters

Homework Statement

With the help of cross product prove: if the angle between the diameters of a parallelogram is 90 degrees, then the parallelogram is a rectangular.

Homework Equations

A\timesB=(surface of the parallelogram)

The Attempt at a Solution

 

[clamtrox]

What is |\mathbf{A} \times \mathbf{B}|? How does it depend on the angle between the two vectors?

 

[rado5]

A and B are not the diameters, they are the sides. As I mensioned |\mathbf{A} \times \mathbf{B}|= (the surface of the parallelogram)

 

[lanedance]

what are the diameters? the diagonals? if so you should be able to write them as a vector sum of the sides...