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JEE Main & Advanced Mathematics Straight Line Question Bank Angle between two straight lines, Bisector of angle between two lines

  • question_answer
    If the coordinates of the vertices A, B, C of the triangle ABC be \[(-\ 4,\ 2),\] \[(12,\ -2)\] and \[(8,\ 6)\]respectively, then \[\angle \ B\]=

    A)            \[{{\tan }^{-1}}\left( -\frac{6}{7} \right)\]

    B)            \[{{\tan }^{-1}}\left( \frac{6}{7} \right)\]

    C)            \[{{\tan }^{-1}}\left( -\frac{7}{6} \right)\]

    D)            \[{{\tan }^{-1}}\left( \frac{7}{6} \right)\]

    Correct Answer: D

    Solution :

    Here equation of AB is \[x+4y-4=0\]                .....(i) and equation of BC is \[2x+y-22=0\]               .....(ii) Thus angle between (i) and (ii) is given by                    \[{{\tan }^{-1}}\frac{-\frac{1}{4}+2}{1+\left( -\frac{1}{4} \right)\text{ }(-2)}={{\tan }^{-1}}\frac{7}{6}\].


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