Question

If $|\overrightarrow{A}-\overrightarrow{B}|=\left|\overrightarrow{A}\right|=\left|\overrightarrow{B}\right|,$ the angle between $\overrightarrow{A}and\overrightarrow{B}$ is

• A. ${60}^{\circ }$
• B. $0$
• C. ${120}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is A ${60}^{\circ }$

$|\overline{A}-\overline{B}|=\left|\overline{A}\right|=\left|\overline{B}\right|$

${|\overline{A}-\overline{B}|}^2={\left|\overline{A}\right|}^2+{\left|\overline{B}\right|}^2-2\left|\overline{A}\right|.\left|\overline{B}\right|\cos \theta$

$⟹{\left|\overline{A}\right|}^2={\left|\overline{A}\right|}^2+{\left|\overline{A}\right|}^2-2{\left|\overline{A}\right|}^2\cos \theta$

$(\because |\overline{A}-\overline{B}|=\left|\overline{A}\right|and\left|\overline{A}\right|=\left|\overline{B}\right|)$

$⟹{\left|\overline{A}\right|}^2=2{\left|\overline{A}\right|}^2\cos \theta$

$⟹\cos \theta =\frac{1}{2}$

$⟹\theta =\frac{\pi }{3}or{60}^{\circ }$

$\therefore A)ans.$