If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

Options

A. `0^(@)`
B. `45^(@)`
C. `90^(@)`
D. `180^(@)`

Answer

C

Explanation

`|vec(p)+vec(q)|= sqrt(p^(2) +q^(2)+2pqcos theta)`
`|vec(p)-vec(q)|= sqrt(p^(2)+q^(2) - 2 pqcos theta)`
`|vec(p) +vec(q)| = |vec(p)-vec(q)|`
`sqrt(p^(2) +q^(2) +2pqcos theta) = sqrt(p^(2) +q^(2) - 2pqcos theta)`
`2 pq cos theta = - 2 pq cos theta`
`4 pq cos theta = 0 `
`sin theta p ne and q ne 0`
`cos theta = 0 `
`:. 0 = 90^(@)`