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

  • question_answer
    Direction ratios of the normal to the plane passing through the points (0, 1, 1), (1, 1, 2) and (?1, 2, ? 2) are

    A)            (1, 1, 1)

    B)            (2, 1, ?1)

    C)            (1, 2, ?1)

    D)            (1, ? 2, ? 1)

    Correct Answer: D

    Solution :

                      \[l\,(1)+m(0)+n(2-1)=0\,\,\Rightarrow \,\,l+n=0\]                    And \[l\,(-2)+m(1)+n(-4)=0\,\,\,\,\Rightarrow \,\,\,2l-m+4n=0\]            \[\therefore \,\,\,l=-\frac{m}{2}=-\,n\].                    Hence direction ratios are\[(1,\,\,-2,\,\,-1)\].


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