Question

Vector $\overrightarrow{R}$ is perpendicular to $\overrightarrow{A}$ as shown in figure and magnitude of $\overrightarrow{R}$ is equal to half of the mangitude of $\overrightarrow{B}$. Find the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$.

• A. ${150}^{\circ }$
• B. ${120}^{\circ }$
• C. ${30}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is A ${150}^{\circ }$

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


We can write,
$\sin \theta =\frac{|\overrightarrow{R}|}{|\overrightarrow{B}|}=\frac{|\overrightarrow{B}|}{2|\overrightarrow{B}|}=\frac{1}{2}\Rightarrow \theta ={30}^{\circ }$ (where, mod represent the magnitude of that vector).
To find angle between two vectors, join them either by tail or head.
Hence, angle between vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $({180}^{\circ }-\theta )$ which is equal to ${180}^{\circ }-{30}^{\circ }={150}^{\circ }$.