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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Self Evaluation Test - Three Dimensional Geometry

  • question_answer
    What are the direction ratios of the line determined by the planes \[x-y+2z=1\] and\[x+y-z=3\]?

    A) (-1, 3, 2)

    B) (-1, -3, 2)

    C) (2, 1, 3)

    D) (2, 3, 2)

    Correct Answer: A

    Solution :

    [a] The intersection of given plane is \[x-y+2z-1+\lambda (x+y-z-3)=0\] \[\Rightarrow x(1+\lambda )+y(\lambda -1)+z(2-\lambda )-3\lambda -1=0\] DR?s of normal to the above plane is \[(1+\lambda ,\lambda -1,2-\lambda )\] By taking option (a) \[-1(1+\lambda )+3(\lambda -1)+2(2-\lambda )=0\] \[\Rightarrow -1-\lambda +3\lambda -3+4-2\lambda =0\] \[\Rightarrow 0=0\] Which is true.


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