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JEE Main & Advanced Mathematics Straight Line Question Bank Concurrency of three lines

  • question_answer
    The three lines \[lx+my+n=0\], \[mx+ny+l=0\], \[nx+ly+m=0\] are concurrent if                                [Pb. CET 2002]

    A)            \[l=m+n\]                                  

    B)            \[m=l+n\]

    C)            \[n=l+m\]                                  

    D)            \[l+m+n=0\]

    Correct Answer: D

    Solution :

               \[\left| \,\begin{matrix}    l & m & n  \\    m & n & l  \\    n & l & m  \\ \end{matrix}\, \right|=0\Rightarrow \left| \begin{matrix}    l+m+n & m & n  \\    l+m+n & n & l  \\    l+m+n & l & m  \\ \end{matrix} \right|=0\]                    Þ \[(l+m+n)\left| \,\begin{matrix}    1 & m & n  \\    1 & n & l  \\    1 & l & m  \\ \end{matrix}\, \right|=0\Rightarrow (l+m+n)=0\].


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