Q. If $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$ and $A = \sqrt{3}$, $B = \sqrt{3}$ and $C = 3$, then the angle between $\overrightarrow{A}\ and\ \overrightarrow{B}$ is
A) 0${^\circ}$
B) 30${^\circ}$
C) 60${^\circ}$
D) 90${^\circ}$
Explanation
(c) $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$ (given)
So, it is given that $\overrightarrow{C}$ is the resultant of $\overrightarrow{A}$ and $\overrightarrow{B}$
$\therefore\ \ \ \ \ C^{2} = A^{2} + B^{2} + 2AB\ cos\theta$
$3^{2} = 3 + 3 + 2 \times 3 \times cos\theta$
3=6 $cos\theta$ or $cos\theta = \frac{1}{2}\ \ \ \ \ \Rightarrow \theta\ 60{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.