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

  • question_answer
    If the lines \[x+q=0,y-2=0\] and \[3x+2y+5=0\] are concurrent, then value of q will be      [DCE 2002]

    A)            1     

    B)            2

    C)            3     

    D)            5

    Correct Answer: C

    Solution :

               Lines are concurrent, if \[\left| \,\begin{matrix}    {{a}_{1}} & {{b}_{1}} & {{c}_{1}}  \\    {{a}_{2}} & {{b}_{2}} & {{c}_{2}}  \\    {{a}_{3}} & {{b}_{3}} & {{c}_{3}}  \\ \end{matrix} \right|=0\]                        Þ \[\left| \,\,\begin{matrix}    1 & 0 & \,\,q  \\    0 & 1 & -2\,  \\    3 & 2 & \,\,5  \\ \end{matrix} \right|\,=\,0\]  Þ \[1\,(5+4)-0+q\,(0-3)=0\]                    Þ \[9-3q=0\] Þ \[q=3.\]


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