Q. Two vectors ${\overrightarrow{a}}_{\ }$and $\overrightarrow{b}$ are at an angle of 60${^\circ}$ with each other. Their resultant makes an angle of 45${^\circ}$ with ${\overrightarrow{a}}_{\ }.$ If $\left| {\overrightarrow{b}}_{\ } \right| = 2$ units, then $\left| {\overrightarrow{a}}_{\ } \right|$ is
A) $\sqrt{3}$
B) $\sqrt{3} - 1$
C) $\sqrt{3} + 1$
D) $\sqrt{3}/2$
Explanation
(b) Tan $45{^\circ} = \frac{2\sin 60{^\circ}}{a + 2\cos 60{^\circ}} = \frac{\sqrt{3}}{a + 1}$
$1 = \frac{\sqrt{3}}{a + 1}$
or $a + 1 = \sqrt{3}$
$a = \sqrt{3} - 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.