Two vectors `vec(a)` and `vec(b)` are such that `|vec(a)+vec(b)|=|vec(a)-vec(b)|`. What is the angle between `vec(a)` and `vec(b)`?

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

D

Explanation

Let `theta` be the angle between the vectors `vec(A)` and `vec(B)`. Then
`|vec(A)+vec(B)|= sqrt(A^(2)+B^(2)+2AB cos theta)`
`|vec(A)-vec(B)|= sqrt(A^(2)+B^(2)-2AB cos theta)`
`|vec(A)+vec(B)|=|vec(A)-vec(B)|`
`:. sqrt(A^(2)+B^(2)+2ABcos theta)=sqrt(A^(2)+B^(2)-2AB cos theta)`
Squarung both side, we get `A^(2)+B^(2)+2AB cos theta= A^(2)+B^(2)-2AB cos theta`
`4AB cos theta=0`
`:. cos theta=0 or theta= (pi)/2`