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JEE Main & Advanced Physics Two Dimensional Motion Question Bank Self Evaluation Test - Motion in a Plane

  • question_answer
    The resultant of vectors \[\overrightarrow{\text{P}}\text{ }\]and \[\overrightarrow{\text{Q}}\] is \[\overrightarrow{\text{R}}\]. On reversing the direction of \[\overrightarrow{\text{Q}}\], the resultant vector becomes \[\overrightarrow{S}\]. Then, correct relation is    

    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 \[{{R}^{2}}={{P}^{2}}+{{Q}^{2}}+2PQ\,\,\cos \theta \text{ }\,\,\,\,\,\,\,\,...(i)\] \[{{S}^{2}}={{P}^{2}}+{{Q}^{2}}-PQ\cos \theta \text{          }...(ii)\] \[\text{Adding equations (i) and (ii) , we get }\] \[{{R}^{2}}+{{S}^{2}}=2\left( {{P}^{2}}+{{Q}^{2}} \right).\]


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