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JEE Main & Advanced Sample Paper JEE Main Sample Paper-16

  • question_answer
    If \[\overrightarrow{a},\overrightarrow{b}\]and \[\overrightarrow{c}\]are non-coplanar vectors such That \[(x+y-3)\overrightarrow{a}+(2x-y+2)\overrightarrow{b}+(2x+y+\lambda )\overrightarrow{c}=\overrightarrow{0}\] holds true for some x and y then \[\lambda \] is

    A) \[\frac{7}{3}\]                                   

    B)  2

    C) \[\frac{-10}{3}\]                                               

    D) \[\frac{5}{3}\]

    Correct Answer: C

    Solution :

    Since \[\overrightarrow{a},\overrightarrow{b}\]and\[\overrightarrow{c}\]are non-coplanar vectors \[x+y-3=0,\]\[2x-y+2=0\]and\[2x+y+\lambda =0\] \[\Rightarrow \]\[\left| \begin{matrix}    1 & 1 & -3  \\    2 & -1 & 2  \\    2 & 1 & \lambda   \\ \end{matrix} \right|=0\Rightarrow \lambda =\frac{-10}{3}\]


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