A) \[{{\cos }^{-1}}\left( \frac{11}{14} \right)\]
B) \[{{\cos }^{-1}}\left( -\frac{11}{14} \right)\]
C) \[\frac{2\pi }{3}\]
D) \[\frac{5\pi }{6}\]
Correct Answer: B
Solution :
We have, \[\frac{P}{3}=\frac{Q}{7}=\frac{R}{5}=\lambda \] (say) \[\Rightarrow \] \[P=3\lambda ,\,\,Q=7\lambda ,\,\,R=5\lambda \] \[\therefore \] \[{{R}^{2}}={{P}^{2}}+{{Q}^{2}}+2PQ\cos \theta \] \[\Rightarrow \] \[-33=42\cos \theta \] \[\Rightarrow \] \[\cos \theta =-\frac{11}{14}\] \[\Rightarrow \] \[\theta ={{\cos }^{-1}}\left( -\frac{11}{14} \right)\]
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