Question

The resultant of two velocity vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is perpendicular to $\overrightarrow{A}$. Magnitude of resultant $\left(\overrightarrow{R}\right)$ is equal to half of magnitude of $\overrightarrow{B}$. Find the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$

• A. ${30}^{\circ }$
• B. ${90}^{\circ }$
• C. ${150}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

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


If resultant $\overrightarrow{R}$ is perpendicular to $\overrightarrow{A}$,
we can write.
$cos\theta =\frac{|\overrightarrow{R}|}{|\overrightarrow{B}|}=\frac{|\overrightarrow{B}|}{2|\overrightarrow{B}|}=\frac{1}{2}\Rightarrow \theta ={60}^{\circ }$
Angle between vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${90}^{\circ }+\theta$ which is equal to ${90}^{\circ }+{60}^{\circ }={150}^{\circ }$.