Question

Let `vecp and vecq` be two unit vectors and α be the angle between them. Then `(vecp + vecq)` will be a unit vector for what value of α?

Options

• `pi/4`

• `pi/2`

• `(pi)/3`

• `(2pi)/3`

Answer 1

`(2pi)/3`

Explanation:

Given: `|vecp| = 1, |vecq| = 1`

for `|vecp + vecq| = 1`

`|vecp + vecq|^2 = 1`

`(vecp + vecq).(vecp + vecq)` = 1

`vecp . vecp + vecp . vecq + vecq . vecp + vecq . vecq = 1`

`|vecp|^2 + 2vecp.vecq + |vecq|^2 = 1 (∵ vecp.vecq = vecp.vecq)`

`1 + 2|vecp||vecq| cos θ + 1 = 1`

2 × 1 × 1 cos θ = 1 − 2

cos θ = `-1/2`

θ = `(2pi)/3`