Let a and b be two vectors such that neither of a - band 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 "a and b are of equal length if and only if the vectors a - b and a + b are perpendicular."