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JEE Main & Advanced Sample Paper JEE Main Sample Paper-21

  • question_answer
    If line contained by the planes \[2x+y+z-3=0\] and \[x-y+2z+5=0\]is parallel to the plane \[mx+2y+3z+1=0,\]then the value of m equals

    A)  1                                

    B)  2

    C)  3                                

    D)  5

    Correct Answer: D

    Solution :

                \[({{\vec{n}}_{1}}\times {{\vec{n}}_{2}})\,.{{\vec{n}}_{3}}\,=0\] (think!)             Where \[{{\vec{n}}_{1}}=\hat{i}-\hat{j}+2\hat{k};\]             \[{{\vec{n}}_{2}}=2\hat{i}+\hat{j}+\hat{k};\] and \[{{\vec{n}}_{3}}=m\hat{i}+2\hat{j}+3\hat{k};\]             \[\left| \begin{matrix}    2 & 1 & 1  \\    1 & -1 & 2  \\    m & 2 & 3  \\ \end{matrix} \right|=0\Rightarrow \,m=5\]


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