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

  • question_answer
    The direction cosines of the normal to the plane \[2x+3y-6z=5\] are

    A)            \[2,\,\,3,\,\,-6\]

    B)            \[\frac{2}{7},\,\frac{3}{7},\,-\frac{6}{7}\]

    C)            \[\frac{2}{5},\,\,\frac{3}{5},\,-\frac{6}{5}\]

    D)            None of these

    Correct Answer: B

    Solution :

               Direction ratios of normal to the plane are (2, 3,  ? 6)                              \[\therefore \] Direction cosines are, \[\left( \frac{2}{\sqrt{49}},\,\frac{3}{\sqrt{49}},\,-\frac{6}{\sqrt{49}} \right)\] or  \[\left( \frac{2}{7},\,\frac{3}{7},\,\frac{-6}{7} \right)\].


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