Q 11-03-017NEETJEE MainMedium
The resultant of two forces $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$, and its magnitude is half the magnitude of $\vec{B}$. The angle between $\vec{A}$ and $\vec{B}$ is
Answer: (B) $150°$
Concept. Resolve the resultant along and across $\vec A$: $(A + B\cos\theta,\ B\sin\theta)$.
Step 1. Perpendicular to $\vec A$. $A + B\cos\theta = 0$, so $\cos\theta < 0$.
Step 2. Magnitude. $R = B\sin\theta = \dfrac{B}{2} \Rightarrow \sin\theta = \dfrac12$.
Step 3. Angle. With $\cos\theta < 0$: $\theta = 150°$.
Answer. $150°$ (Option B).
Solution by Sreeraj P, M.Sc Physics