JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    If O is the origin and A is the point (a, b, c) then the equation of the plane through A and at right angles to OA is                    [AMU 2005]

    A)            \[a(x-a)-b(y-b)-c(z-c)=0\]

    B)            \[a(x+a)+b(y+b)+c(z+c)=0\]

    C)            \[a(x-a)+b(y-b)+c(z-c)=0\]

    D)            None of these

    Correct Answer: C

    Solution :

               Normal will be OA whose direction ratios are \[a-0,\] \[b-0,\] \[c-0\] i.e., a, b, c. It passes through \[A\,(a,\,\,b,\,\,c).\]            \[\therefore \] Equation of required plane is,             \[a\,(x-a)+b\,(y-b)+c\,(z-c)=0\].

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