A) \[P,2P\]
B) \[P,\,\,P\sqrt{3}\]
C) \[2P,\,\,P\sqrt{3}\]
D) None of these
Correct Answer: C
Solution :
Let \[\overrightarrow{OA}={{P}_{1}}\mathbf{i},\] \[\overrightarrow{CB}=-{{P}_{1}}\mathbf{i},\] \[\overrightarrow{OB}=-{{P}_{1}}\mathbf{i}+P\mathbf{j}\] \[\frac{\overrightarrow{OB}\,.\,j}{OB}=\cos 60{}^\circ \Rightarrow \frac{(-{{P}_{1}}i+Pj)\,.\,j}{\sqrt{P_{1}^{2}+{{P}^{2}}}}=\frac{1}{2}\] \[\Rightarrow 2P=\sqrt{{{P}^{2}}+P_{1}^{2}}\Rightarrow {{P}_{1}}=P\sqrt{3}\] \[|\overrightarrow{OB}|\,=\sqrt{{{P}^{2}}+P_{1}^{2}}=\sqrt{{{P}^{2}}+3{{P}^{2}}}=2P.\]You need to login to perform this action.
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