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

  • question_answer
    A line makes angles \[\alpha ,\beta ,\gamma \] with the co-ordinate axes. If \[\alpha +\beta ={{90}^{o}}\],  then \[\gamma =\]

    A)            0

    B)            \[90{}^\circ \]

    C)            \[180{}^\circ \]

    D)            None of these

    Correct Answer: B

    Solution :

               Here, \[{{\cos }^{2}}\alpha +{{\cos }^{2}}(90-\alpha )+{{\cos }^{2}}\gamma =1\]                    Þ  \[{{\cos }^{2}}\alpha +{{\sin }^{2}}\alpha +{{\cos }^{2}}\gamma =1\]            Þ  \[{{\cos }^{2}}\gamma +1=1\,\,\Rightarrow \,\,\gamma ={{90}^{o}}\].


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