JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    A point moves so that its distances from the points (3, 4, ?2) and (2, 3, ? 3) remains equal. The locus of the point is

    A)            A line

    B)            A  plane whose normal is equally inclined to axes 

    C)            A plane which passes through the origin

    D)            A sphere

    Correct Answer: B

    Solution :

               According to question,                    \[{{(x-3)}^{2}}+{{(y-4)}^{2}}+{{(z+2)}^{2}}={{(x-2)}^{2}}+{{(y-3)}^{2}}+{{(z+3)}^{2}}\]                    \[\therefore \] The equation reduces to a plane as 2nd degree terms cancel out.                    The equation is \[2x+2y+2z=7,\] hence equally inclined to axes.

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