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
