Q. If the magnitude of the sum of the two vectors is equal to the difference of their magnitudes, then the angle between vectors is
A) 0${^\circ}$
B) 45${^\circ}$
C) 90${^\circ}$
D) 180${^\circ}$
Explanation
(d) $\sqrt{P^{2} + Q^{2} + 2PQcos\theta} = (P - Q)$
$\Rightarrow \ \ P^{2} + Q^{2} + 2PQcos\theta = P^{2} + Q^{2} - 2PQ$
$\Rightarrow \ 2PQ$(1+$cos\theta$)=0
but $2PQ \neq 0$
$\therefore\ 1 + cos\theta = 0$ or $cos\theta = - 1$
or $\theta = 180{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.