for equilibrium :

\(\frac{P}{\sin p}=\frac{Q}{\sin q}=\frac{R}{\sin r}\)

where,

\(p =\) Angle between \(Q\) AND \(R =120^{\circ}\)

\(r=\) Angle between \(P\) AND \(Q=150^{\circ}\)

\(q =\) Angle between \(P\) AND \(R =360^{\circ}-\left(120^{\circ}+150^{\circ}\right)\)

\(=90^{\circ}\)

hence.

\(P: Q: R=\sin p: \sin q: \sin r\)

\(=\sin 120^{\circ}: \sin 90^{\circ}: \sin 150^{\circ}\)

\(=\frac{\sqrt{3}}{2}: \frac{1}{2}: \frac{1}{1}\)

\(\therefore \quad \sqrt{3}: 1: 2\)