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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

  • question_answer
    If the vectors\[2\hat{i}+\hat{j}-\hat{k}\]and\[\hat{i}-4\hat{j}+\lambda \hat{k}\]are perpendicular to each other, then\[\lambda \]is equal to

    A)  0               

    B)  \[-1\]

    C)  \[-2\]             

    D)  \[-3\]

    Correct Answer: C

    Solution :

     Let\[\overrightarrow{a}=2\hat{i}+\hat{j}-\hat{k}\]and\[\overrightarrow{b}=\hat{i}-4\hat{j}+\lambda \hat{k}\] Since,\[\overrightarrow{a}\]and\[\overrightarrow{b}\]are perpendicular each other \[\therefore \] \[\overrightarrow{a}.\overrightarrow{b}=0\] \[\Rightarrow \] \[(2\hat{i}+\hat{j}-\hat{k}).(\hat{i}-4\hat{j}+\lambda \hat{k})=0\] \[\Rightarrow \] \[2-4-\lambda =0\] \[\Rightarrow \] \[-\lambda -2=0\] \[\Rightarrow \] \[\lambda =-2\]


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