Question

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors such that $\overrightarrow{a}+\overrightarrow{b}$ is also a unit vector, then find the angle between $\overrightarrow{a}$ and $\overrightarrow{b}.$

Answer 1

Let the angle between vectors $a$ and $b$ be $\theta$

Dot product of $a$ and $b$ is $a.b=|a||b|cos\theta$ , given that $a$ and $b$ are unit vectors .

So $|a|=|b|=1.$

$|a+b{|}^2=|a{|}^2+|b{|}^2+2|a||b|cos\theta$

Therefore $\frac{-1}{2}=cos\theta$ , which implies $\theta =\frac{2\pi }{3}.$