JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    If a plane cuts off intercepts ?6, 3, 4 from the co-ordinate axes, then the length of the perpendicular from the origin to the plane is 

    A)            \[\frac{1}{\sqrt{61}}\]

    B)            \[\frac{13}{\sqrt{61}}\]

    C)            \[\frac{12}{\sqrt{29}}\]

    D)            \[\frac{5}{\sqrt{41}}\]

    Correct Answer: C

    Solution :

                Equation is \[\frac{x}{-6}+\frac{y}{3}+\frac{z}{4}=1\] or \[-2x+4y+3z=12\]                    \[\therefore \] Length of perpendicular from origin                    \[=\frac{12}{\sqrt{4+16+9}}=\frac{12}{\sqrt{29}}\].

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