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JEE Main & Advanced JEE Main Paper (Held On 10-Jan-2019 Evening)

  • question_answer
    If \[\overrightarrow{\alpha }=(\lambda -2)\overrightarrow{a}+\overrightarrow{b}\,\,and\,\,\overrightarrow{\beta }=(4\lambda -2)\overrightarrow{a}+3\overrightarrow{b}\] be two given vectors where vectors \[\overrightarrow{a}\] and \[\overrightarrow{b}\] are non-collinear. The value of \[\lambda \] which vectors \[\overrightarrow{a}\] and \[\overrightarrow{b}\] are collinear, is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

    A) 4                                             

    B) 3     

    C) - 3       

    D)                  - 4

    Correct Answer: D

    Solution :

    \[\overrightarrow{\alpha }\,\,=\,\mu \overrightarrow{\beta }\] \[\text{(}\lambda \,\text{-}\,\text{2)}\,\overrightarrow{\text{a}}\text{+}\overrightarrow{\text{b}}\,\,=\,\mu [(4\lambda -2)\,\overrightarrow{a}\,+\,3\overrightarrow{b}]\,\] \[\lambda \,\text{-}\,\text{2}\,\,\text{=}\,\,\mu (4\lambda -2)\,\,\] \[\Rightarrow \,\,1\,\,=\,\,3\mu \] \[\Rightarrow \,\,\,\mu \,\,=\,\,\frac{1}{3}\] \[\Rightarrow \,\,\,\lambda -2=\frac{1}{3}(4\lambda -2)\] \[\Rightarrow \,\,\,3\lambda -6=\,\,4\lambda -2\] \[\Rightarrow \,\,\,\,-\lambda =4\]


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