Q 11-03-060JEE MainJEE Main 2024 (4 Apr, Shift 1)Medium
Two forces $\vec F_1$ and $\vec F_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec F_1$ and $\vec F_2$ is $\cos^{-1}\left(\dfrac1n\right)$. The value of $|n|$ is ______.
Numerical value type. Enter your answer.
Answer: 6
Let the forces be $F$ and $3F$ with resultant $3F$:
$$(3F)^2 = F^2 + (3F)^2 + 2(F)(3F)\cos\theta \Rightarrow 0 = F^2 + 6F^2\cos\theta \Rightarrow \cos\theta = -\frac16$$
So $n = -6$ and $|n| = 6$.
Solution by Sreeraj P, M.Sc Physics