Question

The resultant of two velocity vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is perpendicular to $\overrightarrow{A}$. The angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${150}^{\circ }$. Find $\frac{|\overrightarrow{R}|}{|\overrightarrow{B}|}$ where $\overrightarrow{R}$ is the resultant vector.

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{1}{2}$


If resultant $\overrightarrow{R}$ is perpendicular to $\overrightarrow{A}$,
we can write.
$\cos \theta =\frac{|\overrightarrow{R}|}{|\overrightarrow{B}|}\text{From diagram;}\theta +{90}^{\circ }={150}^{\circ }...\text{(given)}\Rightarrow \theta ={150}^{\circ }-{90}^{\circ }\Rightarrow \theta ={60}^{\circ }$
$\therefore \cos {60}^{\circ }=\frac{|\overrightarrow{R}|}{|\overrightarrow{B}|}=\frac{1}{2}$