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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank System of Co-ordinates, Direction cosines and direction ratios, Projection

  • question_answer
    If \[\alpha ,\,\,\beta ,\,\gamma \]be the angles which a line makes with the positive direction of co-ordinate axes, then             \[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma =\] [RPET 2000; AMU 2002; MP PET 1989, 98, 2000, 03, Pb. CET 2001]

    A)            2

    B)            1

    C)            3

    D)            0

    Correct Answer: A

    Solution :

               Since \[{{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\]\[\,\Rightarrow \,\Sigma {{\sin }^{2}}\alpha =3-1=2\].


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