A) \[~{{R}^{2}}+{{S}^{2}}=({{P}^{2}}+{{Q}^{2}})\]
B) \[{{R}^{2}}+{{S}^{2}}={{P}^{2}}+{{Q}^{2}}\,\]
C) \[{{R}^{2}}+{{P}^{2}}={{S}^{2}}+{{Q}^{2}}\]
D) \[{{P}^{2}}+{{S}^{2}}=2\,({{Q}^{2}}+{{R}^{2}})\]
Correct Answer: A
Solution :
[a] We have \[{{R}^{2}}={{P}^{2}}+{{Q}^{2}}+2PQ\,\,\cos \theta \text{ }\,\,\,\,\,\,\,\,...(i)\] \[{{S}^{2}}={{P}^{2}}+{{Q}^{2}}-PQ\cos \theta \text{ }...(ii)\] \[\text{Adding equations (i) and (ii) , we get }\] \[{{R}^{2}}+{{S}^{2}}=2\left( {{P}^{2}}+{{Q}^{2}} \right).\]You need to login to perform this action.
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