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JEE Main & Advanced JEE Main Paper (Held On 19 May 2012)

  • question_answer
    If the three planes \[x=5,2x-5a+3z-2=0\]and \[3bx+y-3z=0\] contain a common line, then (a, b) is equal to     JEE Main  Online Paper (Held On 19  May  2012)

    A) \[\left( \frac{8}{15},-\frac{1}{5} \right)\]

    B)                        \[\left( \frac{1}{5},-\frac{8}{15} \right)\]

    C)                        \[\left( -\frac{8}{15},\frac{1}{5} \right)\]                               

    D)                        \[\left( -\frac{1}{5},\frac{8}{15} \right)\]

    Correct Answer: B

    Solution :

                    Let the direction ratios of the common line be \[\ell \], wand n. \[\therefore \]\[\ell \times 1+m\times 0+n\times 0=0\Rightarrow \ell =0\]          ?(1) \[2\ell -5ma+3n=0\Rightarrow 5ma-3n=0\]          ?(2) \[3\ell b+m-3n=0\Rightarrow m-3n=0\]                 ?(3) Subtracting (3) from (1), we get\[m(5a-1)=0\] Now, value of m can not be zero because if w = 0 then w = 0\[\Rightarrow \ell =m=n=0\] which is not possible. Hence, \[5a-1=0\Rightarrow a=\frac{1}{5}\] Thus, option (b) is correct.


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