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JEE Main & Advanced Sample Paper JEE Main Sample Paper-27

  • question_answer
    If the lines \[Li:x-2y+4z=0,\,\,2x+y+z-4=0\] and \[{{L}_{2}}:\frac{x-2}{2}=\frac{y}{1}=\frac{z-1}{2a}\] are perpendicular, then a is equal to

    A)  \[\frac{-1}{2}\]                        

    B)  \[\frac{1}{2}\]

    C)  \[2\]                            

    D)  \[-2\]   

    Correct Answer: D

    Solution :

    Direction ratio of line \[{{L}_{1}}\] is \[\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    1 & -2 & 4  \\    2 & 1 & 1  \\ \end{matrix} \right|\] \[=-6\hat{i}+7\hat{j}+5\hat{k}\] \[\therefore \,\,{{L}_{1}}\bot {{L}_{2}}\Rightarrow \,2(-6)\,+7(1)\,+2a(5)=0\] \[\Rightarrow \,\,a=\frac{1}{2}\]


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