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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Critical Thinking

  • question_answer
    The equation of the plane passing through the points \[(1,-3,-2)\] and perpendicular to planes \[x+2y+2z=5\] and \[3x+3y+2z=8\], is [AISSE 1987]

    A) \[2x-4y+3z-8=0\]

    B) \[2x-4y-3z+8=0\]

    C) \[2x+4y+3z+8=0\]

    D) None of these

    Correct Answer: A

    Solution :

    • \[l+2m+2n=0,\,\,\,3l+3m+2n=0\],\[{{l}^{2}}+{{m}^{2}}+{{n}^{2}}=1,\] we get l, m, n from these equations and then putting the values in \[l(x-1)+m(y+3)\] \[+n(z+2)=0,\] we get the required result.           
    • Trick: Checking conversely,           
    • \[2\,(1)-4\,(-3)\]\[+3(-2)-8=0,\]           
    • So, it passes through given point.                   
    • \[1(2)+2(-4)+2(3)=0,\]           
    • So, it is perpendicular to \[x+2y+2z=5\].                   
    • \[3(2)+3(-4)+2(3)=0,\]           
    • So, it is perpendicular to \[3x+3y+2z=8.\]


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