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

  • question_answer
    If the plane \[3x+y+ 2z + 6 = 0\] is parallel to the line \[\,\frac{3x-1}{2b}=3-y=\frac{z-1}{a}\], then the value of \[3a +3b\] is

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

    B)   \[\frac{3}{2}\]

    C)   3                                 

    D)   4

    Correct Answer: B

    Solution :

    Given plane \[3x+y+2z+6=0\] and line \[\frac{x-1/3}{2b/3}=\frac{y-3}{-1}=\frac{z-1}{a}\] Since plane is parallel to line, then \[3\left( \frac{2b}{3} \right)+\left( 1 \right)\left( -1 \right)+2\left( a \right)=0\] \[\Rightarrow \,\,\,2b-1+2a=0\,\,\Rightarrow \,\,a+b=1/2\] Now, \[3a+3b=3/2\]


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