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

  • question_answer
    The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12N. The magnitude of the two forces are                                                                                                           [AIEEE 2002]

    A) 13, 5

    B) 12, 6

    C) 14, 4      

    D) 11, 7

    Correct Answer: A

    Solution :

    \[P+Q=18,\,\,R=12,\,\,\theta ={{90}^{o}}\],  (say)                 \[\tan \,\theta =\tan {{90}^{o}}=\infty \] \[\Rightarrow \,\,\,P+Q\,\cos \,\alpha =0\],  \[\therefore \,\,\cos \alpha =\frac{-P}{Q}\] Also, \[{{(12)}^{2}}={{P}^{2}}+{{Q}^{2}}+2PQ\,\,\cos \alpha \] or      \[144={{P}^{2}}+{{Q}^{2}}+(2P)(-P)\] \[\Rightarrow \,\,\,144={{Q}^{2}}-{{P}^{2}}=(Q+P)(Q-P)\] or   \[144=18\,(Q-P)\] or  \[Q-P=8\] After solving Q = 13,  P = 5.         


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