The sum, difference and cross produce of two vectors `A` and `B` are mutually perpendicular if

Options

A. `vec(A)` and `vec(B)` are perpendicular to each other and modulus of `vec(A)` is equal to modulus of `vec(B)`.
B. `vec(A)` and `vec(B)` are perpendicular to each other
C. `vec(A)` and `vec(B)` are perpendicular but magnitudes are orbitrary.
D. modulus of `vec(A)` = modulus of `vec(B)` and their directions are arbitrary.

Answer

D

Explanation

`(vec(A) + vec(B)).(vec(A) - vec(B)) = 0 [ :. "two vectors are perpendicular"]`
`A^(2) - B^(2) = 0`
`A = B`
Also `vec(A) + vec(B)` & `vec(A) - vec(B)` are in plane of `vec(A)` & `vec(B)` whereas `vec(A) xx vec(B)` is perpendicular of both of them.