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

  • question_answer
    The lines \[2x+y-1=0,ax+3y-3=0\] and \[3x+2y-2=0\] are concurrent for             [EAMCET 1994]

    A)            All a                                           

    B)            \[a=4\]only

    C)            \[-1\le a\le 3\]                         

    D)            \[a>0\]only

    Correct Answer: A

    Solution :

               Given lines are concurrent, if \[\left| \,\begin{matrix}    2 & 1 & -1  \\    a & 3 & -3  \\    3 & 2 & -2  \\ \end{matrix}\, \right|=0\,\,\].                    This is true for all values of a because\[{{C}_{2}}\]and \[{{C}_{3}}\]are identical.


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