If for two vectors `vec(A)` and `vec(B)`, sum `(vec(A)+vec(B))` is perpendicular to the difference `(vec(A)-vec(B))`. Find the ratio of their magnitude.

Options

A. 1
B. 2
C. 3
D. None of these

Answer

A

Explanation

`(vec(A)+vec(B))` is perpendicular to `(vec(A)-vec(B))`. Thus
`(vec(A)+vec(B)).(vec(A)-vec(B))=0`
or `A^(2)+vec(B).vec(A)-vec(A).vec(B)-B^(2)=0`
Because of communative property of dot product `vec(A).vec(B)= vec(B).vec(A)`
`:. A^(2)-B^(2)=0 or A= B`
Thus the ratio of magnitudes `A//B= 1`