JEE Main & Advanced AIEEE Solved Paper-2006

  • question_answer
    The two lines\[x=ay+b,z=cy+d\]and\[x=a'y+b',z=c'y+d'\]are perpendicular to each other, if     AIEEE  Solved  Paper-2006

    A) \[aa'+cc'=1\]     

    B)        \[\frac{a}{a'}\,+\frac{c}{c'}\,=-1\]            

    C)        \[\frac{a}{a'}\,+\frac{c}{c'}\,=1\]              

    D)        \[aa'+cc'=-1\]

    Correct Answer: D

    Solution :

    Given equations of lines are \[x=ay+b,\text{ }z=cy+d\] and \[x=a'y+b',\text{ }z=c'y+d'\] These equations can be rewritten as \[\frac{x-b}{a}=\frac{y-0}{1}=\frac{z-d}{c}\] and \[\frac{x-b'}{a'}=\frac{y-0}{1}=\frac{z-d'}{c'}\] These lines will perpendicular, if \[aa'+1+cc'=0\]

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