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BCECE Engineering BCECE Engineering Solved Paper-2001

  • question_answer
    The vector \[2\hat{i}+\hat{j}-\hat{k}\]is perpendicular to \[\hat{i}-4\hat{j}+\lambda \hat{k},\]then \[\lambda \] is equal to:

    A)  0                                            

    B)  1                            

    C)  \[-2\]                   

    D)         \[-3\]

    Correct Answer: C

    Solution :

    Key Idea: If a and b are two perpendicular vectors, then their dot product will be zero. Let\[\vec{a}=2\hat{i}+\hat{j}-\hat{k}\]and \[\vec{b}=\hat{i}-4\hat{j}+\lambda \hat{k}.\] Since, \[\vec{a}\]and \[\vec{b}\]are perpendicular \[\therefore \]  \[\vec{a}.\vec{b}=(2\hat{i}+\hat{j}-\hat{k}).(\hat{i}-4\hat{j}+\lambda \hat{k})=0\] \[\Rightarrow \]               \[2-4-\lambda =0\] \[\Rightarrow \]               \[\lambda =-2\]


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