Q. Given, $\overrightarrow{P} = \overrightarrow{A}$ +$\overrightarrow{B}$ and $P = A + B$. The angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is
A) $0{^\circ}$
B) $\frac{\pi}{4}$
C) $\frac{\pi}{2}$
D) $\pi$
Explanation
(a) $\left| \overrightarrow{P} \right| = A + B \Rightarrow \left| \overrightarrow{P} \right|^{2} = (A + B)^{2}$
$\left| \overrightarrow{A} + \overrightarrow{B} \right|^{2} = (A + B)^{2}$
or $A^{2} + B^{2} + 2AB\ cos\theta = A^{2} + B^{2} + 2AB$
or $cos\theta = 1$ or $\theta\text{=}0{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.