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

  • question_answer
    If the direction ratios of a line are \[1,-3,\,2\], then the direction cosines of the line are            [MP PET 1997, Pb. CET 2002]

    A)            \[\frac{1}{\sqrt{14}},\frac{-3}{\sqrt{14}},\frac{2}{\sqrt{14}}\]

    B)            \[\frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}\]

    C)            \[\frac{-1}{\sqrt{14}},\frac{3}{\sqrt{14}},\frac{-2}{\sqrt{14}}\]

    D)            \[\frac{-1}{\sqrt{14}},\frac{-2}{\sqrt{14}},\frac{-3}{\sqrt{14}}\]

    Correct Answer: A

    Solution :

               For D'ratio (1, ? 3, 2), the direction cosine will be \[\left( \frac{1}{\sqrt{1+9+4}},\,\frac{-3}{\sqrt{1+9+4}},\,\frac{2}{\sqrt{1+9+4}} \right)\]                    \[\Rightarrow \,\,\left( \frac{1}{\sqrt{14}},\,\frac{-3}{\sqrt{14}},\,\frac{2}{\sqrt{14}} \right)\].


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