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JEE Main & Advanced Sample Paper JEE Main Sample Paper-41

  • question_answer
    If the lines \[\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\]and \[\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}\]intersect, then the value of k is                              

    A)  \[\frac{3}{2}\]                                   

    B)  \[\frac{9}{2}\]

    C)  \[-\frac{9}{2}\]                                 

    D)  \[-\frac{3}{2}\]

    Correct Answer: B

    Solution :

    Since, the lines intersect, therefore they must have a point in common, ie, \[\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}=\lambda \]                        (say) and\[\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{4}=\mu \]                   (say) \[\Rightarrow \]\[x=2\lambda +1,y=3\lambda -1,z=4\lambda +1\]and \[x=\mu +3,y=2\mu +k,z=\mu \]are same. \[\therefore \]\[2\lambda +1=\mu +3,3\lambda -1=2\mu +k\]and\[4\lambda +1=\mu \] On solving these, we get \[\lambda =-\frac{3}{2}\]and\[\mu =-5\] \[\therefore \]    \[k=3\lambda -2\mu -1\]             \[=3\left( -\frac{3}{2} \right)-2(-5)-1\] \[\therefore \]    \[k=\frac{9}{2}\]


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