Question

$\overline{a},\overline{b}$ and $\overline{c}$ are unit vector such that $\overline{a}+\overline{b}-\overline{c}=0$. then the angle between $\overline{a}$ and $\overline{b}$ is :-

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{2}$
• D. $\frac{2\pi }{3}$

Answer 1

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

$\overline{a}+\overline{b}-\overline{c}=0$

$\overline{a}+\overline{b}=\overline{c}$

$|\overline{a}+\overline{b}|=|\overline{c}|=1$

$a^2+b^2+2abcos\theta =1$

$1+1+2cos\theta =1$

$2cos\theta =-1$

$cos\theta =-1/2$

So $\theta =2\pi /3$