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

  • question_answer
    The equation of the plane through the intersection of the planes \[x+2y+3z-4=0\], \[4x+3y+2z+1=0\] and passing through the origin will be [MP PET 1998]

    A) \[x+y+z=0\]

    B) \[17x+14y+11z=0\]

    C) \[7x+4y+z=0\]

    D) \[17x+14y+z=0\]

    Correct Answer: B

    Solution :

    • Equation of plane passing through intersecting the planes \[x+2y+3z-4=0\] and \[4x+3y+2z+1=0\] is, \[x+2y+3z-4+\lambda \,(4x+3y+2z+1)=0\]           
    • Since it is passing through origin, so \[\lambda =4.\]                   
    • Hence the required equation is \[17x+14y+11z=0.\]


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