JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Line

  • question_answer
    The angle between the lines \[2x=3y=-z\] and \[6x=-y=-4z\],  is [MP PET 1994, 99; AIEEE 2005]

    A)                                                               \[0{}^\circ \]

    B)                                                               \[30{}^\circ \]

    C)                                                               \[45{}^\circ \]

    D)                                                               \[90{}^\circ \]

    Correct Answer: D

    Solution :

                    The lines are \[\frac{x}{3}=\frac{y}{2}=\frac{z}{-6}\] and \[\frac{x}{2}=\frac{y}{-12}=\frac{z}{-3}\] Since, \[{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}=6-24+18=0\,\,\Rightarrow \,\,\theta ={{90}^{o}}\].


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