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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 a straight line in space is equally inclined to the co-ordinate axes, the cosine of its angle of inclination to any one of the axes is                                                                            [MP PET 1992]

    A)            \[\frac{1}{3}\]

    B)            \[\frac{1}{2}\]

    C)            \[\frac{1}{\sqrt{3}}\]

    D)            \[\frac{1}{\sqrt{2}}\]

    Correct Answer: C

    Solution :

               Here, \[\cos \alpha =\cos \beta =\cos \gamma \]             \[\therefore \] \[3\,{{\cos }^{2}}\alpha =1\,\,\Rightarrow \,\,\alpha ={{\cos }^{-1}}\left( \pm \frac{1}{\sqrt{3}} \right)\].


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