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)) bot (vec(A)- vec(B))`
`(vec(A) + vec(B)).(vec(A)- vec(B))= 0`
`rArr vec(A)^(2) + vec(B).vec(A) - vec(A).vec(B)- vec(B)^(2)= 0` [Since, `vec(A).vec(B)= vec(B).vec(A)`]
`rArr vec(A)^(2)- vec(B)^(2)= 0 rArr vec(A) = vec(B)`
Ratio of magnitude `((A)/(B))= 1`