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 line \[\frac{3x+1}{-3}=\frac{3y+2}{6}=\frac{z}{-1}\] are

    A)            \[\left( \frac{1}{3},\frac{2}{3},\,0 \right)\]

    B)            \[\left( -1,\frac{2}{3},\,1 \right)\]

    C)            \[\left( -\frac{1}{2},\,\text{ }1,\,-\frac{1}{2} \right)\]

    D)            \[\left( -\frac{1}{\sqrt{6}},\frac{2}{\sqrt{6}},-\frac{1}{\sqrt{6}} \right)\]

    Correct Answer: D

    Solution :

               Change the given equation in standard form, we get, \[\,\,\frac{x+\frac{1}{3}}{-1}=\frac{y+\frac{2}{3}}{2}=\frac{z}{-1}\]            So direction cosine are,\[\left( \frac{-1}{\sqrt{6}},\,\frac{2}{\sqrt{6}},\frac{-1}{\sqrt{6}} \right)\].


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