This is a neat problem.
If are consecutive sides of a parallelogram then are its diagonals.
Now .
So if the parallelogram is a rhombus then .
What does that imply?
What is the converse?
I proved that ||a+b|| = ||a-b|| if and only if a.b = 0
However the next part says using this explain why a paralleogram is a rhombus if and only if its diagonals are at right angles..
I can't figure this out?