JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    Distance between parallel planes \[2x-2y+z+3=0\] and \[4x-4y+2z+5=0\] is [MP PET 1994, 95]

    A)            \[\frac{2}{3}\]

    B)            \[\frac{1}{3}\]

    C)            \[\frac{1}{6}\]

    D)            2

    Correct Answer: C

    Solution :

                The required distance is given by                    \[\left| \frac{3}{\sqrt{{{2}^{2}}+{{2}^{2}}+{{1}^{2}}}}-\frac{5}{\sqrt{{{4}^{2}}+{{4}^{2}}+{{2}^{2}}}} \right|=\left| 1-\frac{5}{6} \right|=\frac{1}{6}\].

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