JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
     If P be the point (2, 6, 3), then the equation of the  plane through P at right angle to OP, O being the origin, is    [MP PET 2000; Pb. CET 2001]

    A)            \[2x+6y+3z=7\]

    B)            \[2x-6y+3z=7\]

    C)            \[2x+6y-3z=49\]

    D)            \[2x+6y+3z=49\]

    Correct Answer: D

    Solution :

                Distance of point P from origin \[OP=\sqrt{4+36+9}=7\]            Now d.r?s of OP = 2?0, 6 ? 0, 3 ? 0 = 2, 6, 3            \ d.c?s of OP = \[\frac{2}{7},\,\frac{6}{7},\,\frac{3}{7}\]            \Equation of plane in normal form is \[lx+my+nz=p\]                    Þ \[\frac{2}{7}x+\frac{6}{7}y+\frac{3}{7}z=7\] Þ \[2x+6y+3z=49\].

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