Let "a" and "b" be two vectors such that neither of a-b and a+b is the zero vector.
(a) Prove that if the vectors a and b are of equal length, then a-b and a+b are perpendicular.
(b) Prove that if a-b and a+b are perpendicular, then a and b are of equal magnitude.
Your solution should not depend on coordinates, slopes, or the properties of geometric figures; try to use vectors! By the way, note that these are the two separate parts of the statement " and are of equal length if and only if the vectors and are perpendicular."
If I could get an explanation over just an answer it would be greatly appreciated
Sounds to me like your teacher really wants you to think hard and do some research on your own.