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JEE Main & Advanced AIEEE Solved Paper-2010

  • question_answer
      If the vectors \[\overrightarrow{a}=\hat{i}-\hat{j}+2\hat{k},\overrightarrow{b}=2\hat{i}+4\hat{j}+\hat{k}\]and \[\overrightarrow{c}=\lambda \hat{i}-\hat{j}+\mu \hat{k}\]are mutually orthogonal, then \[(\lambda ,\mu )=\]       AIEEE  Solved  Paper-2010

    A) (-3, 2)

    B) (2, -3)  

    C) (-2, 3)                  

    D) (3, -2)

    Correct Answer: A

    Solution :

    \[\overrightarrow{a}\bot \overrightarrow{b}\therefore \overrightarrow{a}.\overrightarrow{b}=0\] \[\overrightarrow{b}\bot \overrightarrow{c}\therefore \overrightarrow{b}.\overrightarrow{c}=0\]                                 \[2\lambda +4+\mu =0\]                              ?.(1) \[\overrightarrow{a}\bot \overrightarrow{c}\therefore \overrightarrow{a}.\overrightarrow{c}=0\] \[\lambda -1+2\mu =0\]                                                               ...(2) solving (1) and (2), we get \[\lambda =3\] \[\mu =2\]


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