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JEE Main & Advanced Sample Paper JEE Main Sample Paper-31

  • question_answer
    If the lines \[\frac{1-x}{3}=\frac{7y-14}{2p}=\frac{z-3}{2}\] and \[\frac{7-7x}{3p}=\frac{5-y}{1}=\frac{6-z}{5}\] are orthogonal to each other, then the value of p is

    A) 10    

    B)                                    \[\frac{70}{11}\]

    C) 7                                             

    D) 5

    Correct Answer: A

    Solution :

    The first line is \[\frac{x-1}{-3}=\frac{y-2}{2p/7}=\frac{z-3}{2};\] parallel \[{{\overrightarrow{v}}_{1}}=-3\widehat{i}+\frac{2p}{7}\widehat{j}+2\widehat{k}\]\[1+ba>0\] Second line \[\frac{(x-1)}{-3p/7}=\frac{y-5}{-1}=\frac{z-6}{-5};\] parallel to \[{{\overrightarrow{v}}_{2}}=\frac{3p}{7}\widehat{i}-\widehat{j}-5\widehat{k}\] Now, \[-3.\left( \frac{-3p}{7} \right)+\left( \frac{2p}{7} \right).(-1)+2(-5)=0\] \[\therefore 7p=70\Rightarrow p=10\]


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