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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    The equation of the plane passing through (1, 1, 1) and        (1, ?1, ?1) and perpendicular to \[2x-y+z+5=0\]is [EAMCET 2003]

    A)            \[2x+5y+z-8=0\]

    B)            \[x+y-z-1=0\]

    C)            \[2x+5y+z+4=0\]

    D)            \[x-y+z-1=0\]

    Correct Answer: B

    Solution :

               Any plane passing through (1, 1, 1) is \[a(x-1)+b(y-1)+c(z-1)=0\]                     .....(i)            Plane (i) is also passing through (1, ?1, ?1)            \[\therefore a\,.\,0+b(-2)+c(-2)=0\]            or, \[0.a-2b-2c=0\] or \[0.a-b-c=0\]            or, \[0.a+b+c=0\]                                  ......(ii)            Plane (i) is perpendicular to \[2x-y+z+5=0\]            So, \[2a-b+c=0\]                                   .....(iii)              From (ii) and (iii), \[a=b=1,\,c=-1\]            Substituting in (i) we have \[x+y-z-1=0\].                   


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