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

  • question_answer
     If the direction cosines of a line are \[\left( \frac{1}{c},\frac{1}{c},\frac{1}{c} \right)\],  then  [JET 1989; CET 1993]

    A)            \[c>0\]

    B)            \[c=\pm \sqrt{3}\]

    C)            \[0<c<1\]

    D)            \[c>2\]

    Correct Answer: B

    Solution :

               Since direction cosines of line are \[\left( \frac{1}{c},\frac{1}{c},\frac{1}{c} \right)\]            \[\therefore \,\,\frac{1}{{{c}^{2}}}+\frac{1}{{{c}^{2}}}+\frac{1}{{{c}^{2}}}=1\,\,\Rightarrow \,{{c}^{2}}=3\,\Rightarrow \,\,c=\pm \,\sqrt{3}\].


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