A) \[{{0}^{o}}\]
B) \[{{30}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{90}^{o}}\]
Correct Answer: D
Solution :
Resultant of P and Q, \[R=\sqrt{{{p}^{2}}+{{Q}^{2}}+2\,PQ\cos \theta }\] Here, R = p \[\therefore \] \[p=\sqrt{{{p}^{2}}+{{Q}^{2}}+2\,PQ\cos \theta }\] \[{{p}^{2}}={{p}^{2}}+{{Q}^{2}}+2\,PQ\cos \theta \] \[Q+2\,P\,\cos \theta =0\] \[(\because \,\,p\ne 0)\] Required angle \[\beta ={{\tan }^{-1}}\left[ \frac{p}{Q+p\,\cos \theta } \right]\] \[={{\tan }^{-1}}\left( \frac{2p}{Q+2p\cos \theta } \right)\] \[(\because \,p2p)\] \[={{\tan }^{-1}}\left( \frac{2p}{0} \right)\] \[={{\tan }^{-1}}(\infty )={{90}^{o}}\]
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