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

Options

A. `|ve(a)|=|vec(b)|`
B. `vec(a)` is parallel to `vec(b)`.
C. `vec(a)` is perpendicular to `vec(b)`.
D. `vec(a)` is unit vector.

Answer

C

Explanation

Since, `|a+b|=|a-b|`
`rArr [|a+b|]^(2)=[a-b]^(2)`
`rArr a.a+b.b+a.b+b.a=a.a + b.b-a.b-b.a`
`rArr 4a.b=0 (. :. a.b=b.a)`
`rArr a.b=0`
Hence, a is perpendicular to b.