Let $\vec a$ and $\vec b$ be two unit vectors and $α$ be the angle between them, then $\vec a + \vec b$ is a unit vector, if $α =$

$2π/3$

We have, $|\vec a|=|\vec b|=1$

It is given that

$|\vec a+\vec b|=1$

$⇒|\vec a+\vec b|^2=1$

$⇒|\vec a|^2=|\vec b|^2+2(\vec a.\vec b)=1$

$⇒|\vec a|^2=|\vec b|^2+2|\vec a||\vec b|\cos α=1$

$⇒2+2\cos α=1$  $[∵|\vec a|=1,|\vec b|=1]$

$⇒\cos α=-\frac{1}{2}⇒α=\frac{2π}{3}$