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JEE Main & Advanced JEE Main Paper (Held On 9 April 2017)

  • question_answer
    If \[x=a,\,\,y=b,\,\,z=c\] is solution of the system of linear equations  [JEE Online 09-04-2017]                 \[x+8y+7z=0\] \[9x+2y+3z=0\] \[y+y+z=0\]        such that the point \[(a,\,b,\,c)\] lies on the plane \[x+2y+z=6,\] then \[2a+b+c\] equals:

    A)  2                                            

    B)  - 1

    C)  1                                            

    D)  0

    Correct Answer: A

    Solution :

    \[\left. \begin{align}   & x+8y+7z=0 \\  & 9x+2y+3z=0 \\  & x+y+z=0 \\ \end{align} \right\}\begin{matrix}    7y+6z=0  \\    \begin{align}   &  \\  & 7x+z=0 \\ \end{align}  \\ \end{matrix}\]  \[x=\lambda \,\,\,\,\,\,\,\,\left| y=\frac{-6(-7\lambda )}{7}\, \right|=7=-7gl\] \[\,\,\,\,\,\,\,\,\,\,\,\] \[\lambda +12\lambda -7\lambda =6\,\]\[2\lambda +6\lambda -7\lambda \] \[6\lambda =6\]                                 \[=2\lambda \] \[\]                            \[=\]


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