Question

Let `veca` and `vecb` be two unit vectors and θ is the angle between them, Then `veca + vecb` is a unit vector if-

पर्याय

• `theta = pi/4`

• `theta = pi/3`

• `theta = pi/2`

• `theta = (2pi)/3`

Answer 1

`theta = (2pi)/3`

Explanation:

We have, `|veca|` = 1, `|vecb|` = 1

And `|veca + vecb|` = 1 or `|veca + vecb|^2` = 1

i.e., `(veca + vecb) * (veca + vecb)` = 1

or `|veca|^2 + veca * vecb + vecb * veca + |vecb|^2` = 1

or `|veca|^2 + |vecb|^2 + 2veca * vecb` = 1  ......`[because vecb * veca = veca * vecb]`

= `1 + 1 + 2 |veca| |vecb| cos theta` = 1

Where θ is the angle between `veca` and `vecb`

∴ `2 + 2 cos theta` = 1

or `2 cos 2 theta` = 1

⇒ `cos theta = - 1/2`

∴ `theta = (2pi)/3`.