RAJASTHAN ­ PET Rajasthan PET Solved Paper-2004

  • question_answer
    Three lines\[3x+4y+6=0,\]\[\sqrt{2}x+\sqrt{3}y+2\sqrt{2}=0\]and\[4x+7y+8=0\]are

    A)  sides of a triangle

    B)  concurrent

    C)  parallel       

    D)  None of these

    Correct Answer: B

    Solution :

     Given, lines are\[3x+4y+6=0\] \[\sqrt{2}x+\sqrt{3}y+2\sqrt{2}=0\] and         \[4x+7y+8=0\] \[\therefore \]\[\left| \begin{matrix}    3 & 4 & 6  \\    \sqrt{2} & \sqrt{3} & 2\sqrt{2}  \\    4 & 7 & 8  \\ \end{matrix} \right|=3(8\sqrt{3}-14\sqrt{2})\] \[-4(8\sqrt{2}-8\sqrt{2})+6(7\sqrt{2}-4\sqrt{3})\] \[=24\sqrt{3}-42\sqrt{2}-0+42\sqrt{2}-24\sqrt{3}\] \[=0\] Hence, given lines are concurrent.


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