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KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    Let \[\overrightarrow{a}=(\lambda -2)\overrightarrow{a}+\overrightarrow{b}\] and \[\overrightarrow{\beta }=(4\lambda -2)\overrightarrow{a}+3\overrightarrow{b}\] be two given vectors where a and b are non collinear. The value of \[\lambda \] for which vectors \[\vec{\alpha }\] and \[\vec{\beta }\] are collinear, is:

    A) \[-4\]

    B) \[-3\]

    C) \[4\]

    D) \[3\]

    Correct Answer: A

    Solution :

    \[\overline{\alpha }=(\lambda -2)\overrightarrow{a}+\overrightarrow{b}\]
    \[\overrightarrow{\beta }=(4\lambda -2)\overrightarrow{a}+3\overrightarrow{b}\]
    \[\overrightarrow{\alpha }\]and \[\overrightarrow{\beta }\]are collinear
    \[\left| \begin{matrix}    \lambda -2 & 1  \\    4\lambda -2 & 3  \\ \end{matrix} \right|=0\]
    \[3\lambda -6-4\lambda +2=0\]
    \[-\lambda -4=0\]


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