Question

If a vector and b vector are perpendicular vectors show that
(a + b)2 = (a - b)2​

Answer 1

Answer:

(To denote a vector, I'll use boldface font)

Given: a and b such that a⊥b

To prove: (a+b)^2 = (a-b)^2

Proof:

(a+b)^2=  a·a + 2a·b + b·b = a^2 + 0 + b^2 = a^2 + b^2 -----(1)

(since a⊥b, a·b=0, and a·a=a^2, b·b=b^2 since angle between two parallel vectors is 0)

Similarly,

(a-b)^2 = a·a - 2a·b + b·b = a^2 - 0 + b^2 = a^2 + b^2 ------(2)

From (1) and (2), we get the desired result

(a+b)^2= (a-b)^2

E.O.Q