JEE Main & Advanced Sample Paper JEE Main - Mock Test - 6

  • question_answer
    If the lines \[\frac{1-x}{3}=\frac{y-2}{2\alpha }=\frac{z-3}{2}\]and \[\frac{x-1}{3\alpha }=y-1=\frac{6-z}{5}\]are perpendicular, then the value of \[\alpha \] is

    A) \[\frac{-10}{7}\]            

    B) \[\frac{10}{7}\]

    C) \[\frac{-10}{11}\]

    D) \[\frac{10}{11}\]

    Correct Answer: A

    Solution :

    [a] : The given lines are perpendicular so, vectors  \[{{\vec{b}}_{1}}=-3\hat{i}+2\alpha \hat{j}+2\hat{k}\]and\[{{\vec{b}}_{2}}=3\alpha \hat{i}+\hat{j}-5\hat{k}\]are perpendicular. So\[{{\vec{b}}_{1}}.{{\vec{b}}_{2}}=0\] \[\Rightarrow \]\[-9\alpha +2\alpha -10=0\Rightarrow -7\alpha =10\] \[\Rightarrow \]\[\alpha =-10/7\]

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