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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2008

  • question_answer
    If the planes\[\overrightarrow{r}.(2\hat{i}-\lambda \hat{j}+3\hat{k})=0\]and\[\overrightarrow{r}.(\lambda \hat{i}+5\hat{j}-\hat{k})=0\]are perpendicular to each other, then the value of\[{{\lambda }^{2}}+\lambda \]is

    A)  0                            

    B)         2

    C)  1                            

    D)         3

    E)  4      

    Correct Answer: A

    Solution :

    Since, given planes\[\overrightarrow{r}.(2\hat{i}-\lambda \hat{j}+3\hat{k})=0\]and\[\overrightarrow{r}.(\lambda \hat{i}+5\hat{j}-\hat{k})=5\]are perpendicular. \[\therefore \]  \[2(\lambda )-\lambda (5)+3(-1)=0\] \[\Rightarrow \]               \[-3\lambda -3=0\Rightarrow \lambda =-1\] \[\therefore \]  \[{{\lambda }^{2}}+\lambda ={{(-1)}^{2}}-1\]                                 \[=0\]


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