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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

  • question_answer
    If a, b and c are non-coplanar and\[(a+\lambda b).[(b+3c)\times (c-4a)]=0,\]then the value of\[\lambda \]is equal to

    A)  0

    B)  \[\frac{1}{12}\]

    C)  \[\frac{5}{12}\]

    D)  \[3\]

    Correct Answer: B

    Solution :

    Given, \[(a+\lambda b).[(b+3c)\times (c-4a)]=0\] \[\Rightarrow \]\[(a+\lambda b).[b\times c-4b\times a-12c\times a]=0\] \[\Rightarrow \]\[[a\,b\,c]-0-0+0+0-12\lambda [b\,c\,a]=0\] \[\Rightarrow \] \[[a\,b\,c]=12\lambda [b\,c\,a]\] \[\Rightarrow \] \[\lambda =\frac{1}{12}\]


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