Two forces P and Q , of magnitude 2F and 3F , respectively, are at...

$\left|\overset{\to}{P}\right| = 2F, \left|\overset{\to}{Q}\right| = 3F$

\left|\overset{\to}{R}\right| = \sqrt{{P}^{2} + {Q}^{2} + 2PQcos\theta}$<br /><br />$= \sqrt{4{F}^{2} + 9{F}^{2} + 12{F}^{2}cos\theta} = F\sqrt{13 + 12cos\theta}$<br /><br />If$Q$is doubled<br /><br />$2\left|\overset{\to}{R}\right| = \sqrt{4{F}^{2} + 36{F}^{2} + 24{F}^{2}cos\theta} = F\sqrt{40 + 24cos\theta}$<br /><br />$4\left(13 + 12cos\theta\right) = 40 + 24cos\theta$<br /><br />$12 = - 24cos\theta$<br /><br />$cos\theta = - \dfrac{1}{2}$<br /><br />$\theta = {120}^{°}