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

  • question_answer
    If a line makes the angle \[\alpha ,\beta ,\gamma \] with three dimensional        co-ordinate axes respectively, then \[\cos 2\alpha +\cos 2\beta +\cos 2\gamma =\] [MP PET 1994, 95,99; RPET 2003; Kerala (Engg.) 2005]

    A)            ? 2

    B)            ? 1

    C)            1

    D)            2

    Correct Answer: B

    Solution :

               \[\cos \,2\alpha +\cos \,2\beta +\cos \,2\gamma \]            \[=2\,{{\cos }^{2}}\alpha -1+2\,{{\cos }^{2}}\beta -1+2\,{{\cos }^{2}}\gamma -1\]            \[=2\,({{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma )-3=2-3=-1.\]


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