Question

Given that $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{R}$ and $A=B=R$. What should be the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ ?

• A. $0$
• B. $\frac{\pi }{3}$
• C. $\frac{2\pi }{3}$
• D. $\pi$

Answer 1

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

$R^2=A^2+B^2+2ABcos\theta$
$R^2=R^2+R^2+2R^{2}cos\theta$
$2cos\theta =-1$
$\Rightarrow cos\theta =-\frac{1}{2}\Rightarrow \theta =\frac{2\pi }{3}$