Question

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)

Answer 1

D.90°

Step-by-step 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°