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Three forces $P$, $Q$ and $R$ act at a point in a plane. The angles between $P$ and $Q$, and between $Q$ and $R$ are $150^\circ$ and $120^\circ$ respectively. For equilibrium, the forces $P$, $Q$ and $R$ are in the ratio

1. 1 : 2 : 3
2. 1 : 2 : 3
3. 3 : 2 : 1
4. 3 : 2 : 1

Correct answer: 3 : 2 : 1

Solution

For equilibrium of three concurrent forces, Lami's theorem gives $P/\sin\angle(Q,R)=Q/\sin\angle(R,P)=R/\sin\angle(P,Q)$. Using the given angles, the corresponding sines lead to the ratio $P:Q:R=3:2:1$.

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