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

  • question_answer
    If vertices of a parallelogram are respectively (0, 0), (1, 0), (2, 2) and (1, 2), then angle between diagonals is  [RPET 1996]

    A)            \[\pi /3\]                                     

    B)            \[\pi /2\]

    C)            \[3\pi /2\]                                  

    D)            \[\pi /4\]

    Correct Answer: D

    Solution :

    Here, Slope of Ist  diagonal= \[{{m}_{1}}=\frac{2-0}{2-0}=1\Rightarrow {{\theta }_{1}}={{45}^{o}}\] Slope of IInd diagonal= \[{{m}_{2}}=\frac{2-0}{1-1}=\infty \Rightarrow {{\theta }_{2}}={{90}^{o}}\] Þ\[{{\theta }_{2}}-{{\theta }_{1}}={{45}^{o}}=\frac{\pi }{4}\].


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