If `|vec(a)+vec(b)|=|vec(a)-vec(b)|`, then which one of the following is correct?

Options

A. `vec(a)=lambda vec(b)` for some scalar `lambda`
B. `vec(a)` is parallel to `vec(b)`.
C. `vec(a) ` is perpendicular to `vec(b)`
D. `vec(a)=vec(b)=vec(0)`

Answer

C

Explanation

If `|vec(a)+vec(b)|=|vec(a)-vec(b)|`
We know that when `(vec(a)+vec(b)).(vec(a)-vec(b))=0`, then `vec(a)` is perpendicular to `vec(b)`.
`=vec(a).vec(a)-vec(a).vec(b)+vec(b).vec(a)-vec(b).vec(b)=0`
`vec(a)` is perpendicular to `vec(b)`
`:. ` Option (c) is correct.