Question

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vector and $\theta$ is the angle between them, then $(\overrightarrow{a}+\overrightarrow{b})$ is a unit vector if $\theta =$

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\frac{2\pi }{3}$

Answer 1

The correct option is D $\frac{2\pi }{3}$

Given $|\overrightarrow{a}+\overrightarrow{b}|=1$

$\Rightarrow |\overrightarrow{a}{|}^2+2\overrightarrow{a}\cdot \overrightarrow{b}+|\overrightarrow{b}{|}^2=1$, square both sides

$\Rightarrow 1+2|\overrightarrow{a}||\overrightarrow{b}|\cos \theta +1=1$

$\Rightarrow \cos \theta =-\frac{1}{2}$

$\therefore \theta =\frac{2\pi }{3}$