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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        If a, b and c are non-coplanar vectors and\[\lambda \]is a real number, then the vectors\[2a+2b+3c,\]\[\lambda b+4c\]and\[(\lambda -1)c\]are non-coplanar for

    A)  all except two values of\[\lambda \]

    B)  all except one value of\[\lambda \]

    C)  all values of\[\lambda \]

    D)  no value of\[\lambda \]

    Correct Answer: A

    Solution :

                    For non-coplanarity, \[\left| \begin{matrix}    1 & 2 & 3  \\    0 & \lambda  & 4  \\    0 & 0 & 2\lambda -1  \\ \end{matrix} \right|\ne 0\] \[\Rightarrow \]               \[\lambda (2\lambda -1)\ne 0\] \[\Rightarrow \]               \[\lambda \ne 0,\frac{1}{2}\]


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