Question

The sum and difference of two perpendicular vectors of equal length are also perpendicular to each other and are of equal lengths. Prove that

Answer 1

(A vector + B Vector). (A vector - B vector) =0
(a²-b²=(a+b) (a-b))
(A vector) ²-( B vector) ²=0, (A.B. Vector = AB cos thita)
(A vector)²=(B vector) ²
So A vector =B vector