Q 11-03-146JEE MainJEE Main 2020 (7 Jan, Shift 2)Easy
The sum of two forces $\vec P$ and $\vec Q$ is $\vec R$ such that $|\vec R| = |\vec P|$. The angle (in degrees) between the resultant of $2\vec P$ and $\vec Q$ and the force $\vec Q$ is ______.
Numerical value type. Enter your answer.
Answer: 90
$|\vec P + \vec Q|^2 = P^2 \Rightarrow P^2 + 2\vec P\cdot\vec Q + Q^2 = P^2 \Rightarrow 2\vec P\cdot\vec Q = -Q^2$.
$$(2\vec P + \vec Q)\cdot\vec Q = 2\vec P\cdot\vec Q + Q^2 = 0$$
So $2\vec P + \vec Q$ is perpendicular to $\vec Q$: the angle is $90^\circ$.
Solution by Sreeraj P, M.Sc Physics