Two vectors have a sum A and their difference is B. If A=B then, the angle between the two vectors is

a) 0 b) 45 c) 120 d) 90

(all the options are in degree)

D. 90°

Explanation:

First remember that the magnitude of a vector, lets say T is the square of the dot product with itself.

This is to say

|T|=√ (T*T)

Assume A≠0 and B≠0 then

Square both sides of the below equation

|A+B|²=|A-B|²

(A+B) ² = (A-B) ²

A (A+B) + B (A+B) = A (A-B) - B (A-B)

A²+AB+AB+B²=A²-AB-AB+B²

A²+2AB+B²=A²-2AB+B²

You notice that it simplifies to

2AB = - 2AB

This means that A*B = 0

Hence the angle between the vectors should be 90°