The sum , difference and cross product of two vector A and B are mutually perpendicular if A and B are perpendicular to each other and |A| = |B| This is rig

Question

The sum , difference and cross product of two vector A and B are mutually perpendicular if 

 

A and B are perpendicular to each other and |A| = |B| 

 

This is right or wrong ?

 

If wrong then what is right ?

Answer 1

This is right.  Since A and B are perpendicular and equal in size,  A + B and A - B form the two diagonal lines of a square with A and B its two adjacent sides,  therefore A + B and A - B are perpendicular.   

 

A x B is perpendicular to the plane formed by A + B and A - B,  hence A x B is perpendicular to both A + B and A - B.