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J & K CET Engineering J and K - CET Engineering Solved Paper-2009

  • question_answer
    The equation of the plane passing through the point \[(1,1,1)\] and containing the line of intersection of the planes \[x+y+z=6\] and \[2x+3y+4z=12\] is

    A)  \[x+y+z=3\]

    B)  \[x+2y+3z=6\]

    C)  \[2x+3y+4z=9\]

    D)  \[3x+4y+5z=18\]

    Correct Answer: B

    Solution :

    Equation of  plane containing the line of intersection of planes is \[(x+y+z-6)+\lambda (2x+3y+4z-12)=0\] Since, it passes through the point \[(1,1,1)\]. \[\therefore \]  \[(1+1+1-6)+\lambda (2+3+4-12)=0\] \[\Rightarrow \] \[-3+\lambda (-3)=0\] \[\Rightarrow \] \[\lambda =-1\] Hence, required equation of plane is \[(x+y+z-6)-(2x+3y+4z-12)=0\] ie, \[x+2y+3z=6\]


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