Let $\vec{a}$ and $\vec{b}$ be two unit vectors and $\theta $ is the angle between them. If $\vec{a} +\vec{b}$ is a unit vector, then $\theta $ is :
Answer & explanation
Correct answer: option 1
$|\vec a+\vec b|=1$
so $|\vec a|+|\vec b|+2\vec a.\vec b=1^2$ (Squaring both sides)
so $2+2|\vec a||\vec b|\cos θ=1$
$\cos θ=-\frac{1}{2}⇒θ=\frac{2\pi }{3}$