Question

The resultant of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is perpendicular to $\overrightarrow{A}$. Magnitude of resultant $\overrightarrow{R}$ is equal to $\frac{\sqrt{3}}{2}$ times of the magnitude of $\overrightarrow{B}$. Find the angle between $\overrightarrow{A}$ and $\overrightarrow{B}.$

• A. ${120}^{\circ }$
• B. ${90}^{\circ }$
• C. ${60}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is A ${120}^{\circ }$

Figure shows three vectors $\overrightarrow{A},\overrightarrow{B}$ and $\overrightarrow{R}$, in which $\overrightarrow{R}$ is perpendicular to $\overrightarrow{A}.$

$\sin \theta =\frac{|\overrightarrow{R}|}{|\overrightarrow{B}|}=\frac{\sqrt{3}|\overrightarrow{B}|}{2|\overrightarrow{B}|}\sin \theta =\frac{\sqrt{3}}{2}\Rightarrow \theta ={60}^{\circ }$

Hence, the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${180}^{\circ }-{60}^{\circ }={120}^{\circ }$