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JEE Main & Advanced Mathematics Vector Algebra Question Bank Modulus of vector Algebra of vectors

  • question_answer
    If the resultant of two forces of magnitudes P and Q acting at a point at an angle of \[{{60}^{o}}\] is \[\sqrt{7}Q,\] then P/Q is                                                                                     [Roorkee 1999]

    A) 1             

    B) \[\frac{3}{2}\]

    C) 2             

    D) 4

    Correct Answer: C

    Solution :

    \[{{R}^{2}}={{P}^{2}}+{{Q}^{2}}+2PQ\,\,\cos \theta \] Þ   \[{{(\sqrt{7}Q)}^{2}}={{P}^{2}}+{{Q}^{2}}+2PQ\cos 60{}^\circ \] Þ   \[7{{Q}^{2}}={{P}^{2}}+Q+PQ\] Þ \[{{P}^{2}}+PQ-6{{Q}^{2}}=0\] Þ   \[{{P}^{2}}+3PQ-2PQ-6{{Q}^{2}}=0\] Þ   \[P(P+3Q)-2Q(P+3Q)=0\] Þ   \[(P-2Q)(P+3Q)=0\] Þ   \[P-2Q=0\] or \[P+3Q=0\] From \[P-2Q=0\] Þ \[\frac{P}{Q}=2\].


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