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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2010

  • question_answer
    Which one of the following vectors is of magnitude 6 and perpendicular to both \[\overrightarrow{a}=2\hat{i}+2\hat{j}+\hat{k}\]and\[\overrightarrow{b}=\hat{i}-2\hat{j}+2\hat{k}?\]

    A)  \[2\hat{i}+\hat{j}-2\hat{k}\]                     

    B)  \[2(2\hat{i}-\hat{j}+2\hat{k})\]

    C)  \[3(2\hat{i}-\hat{j}-2\hat{k})\]

    D)         \[2(2\hat{i}+\hat{j}-2\hat{k})\]

    E)  \[2(2\hat{i}-\hat{j}-2\hat{k})\]

    Correct Answer: E

    Solution :

    Required vector \[=\overrightarrow{a}\times \overrightarrow{b}=\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    2 & 2 & 1  \\    1 & -2 & 2  \\ \end{matrix} \right|\] \[=\hat{i}(4+2)-\hat{j}(4-1)+\hat{k}(-4-2)\] \[=6\hat{i}-3\hat{j}-6\hat{k}\] \[=3(2\hat{i}-\hat{j}-2\hat{k})\] But its magnitude is not 6. Therefore correct answer is \[2(2\hat{i}-\hat{j}-2\hat{k})\]


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