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JEE Main & Advanced Sample Paper JEE Main Sample Paper-24

  • question_answer
    If \[\vec{a}=\hat{i}+\hat{j}+\hat{k}\],  \[\vec{b}=\hat{i}-\hat{j}+\hat{k}\], \[\vec{c}=\hat{i}+2\hat{j}-\hat{k}\]then the value of \[\left| \begin{matrix}    \vec{a}.\vec{a} & \vec{a}.\vec{b} & \vec{a}.\vec{c}  \\    \vec{a}.\vec{b} & \vec{b}.\vec{b} & \vec{b}.\vec{c}  \\    \vec{a}.\vec{c} & \vec{b}.\vec{c} & \vec{c}.\vec{c}  \\ \end{matrix} \right|\] is equal to

    A)  18                               

    B)  16

    C)  10                               

    D)  8

    Correct Answer: B

    Solution :

    We have \[\left| \begin{matrix}    \vec{a}.\vec{a} & \vec{a}.\vec{b} & \vec{a}.\vec{c}  \\    \vec{a}.\vec{b} & \vec{b}.\vec{b} & \vec{b}.\vec{c}  \\    \vec{a}.\vec{c} & \vec{b}.\vec{c} & \vec{c}.\vec{c}  \\ \end{matrix} \right|={{[\vec{a}\,\,\vec{b}\,\,\vec{c}]}^{2}}\] \[={{\left| \begin{matrix}    1 & 1 & 1  \\    1 & -1 & 1  \\    1 & 2 & -1  \\ \end{matrix} \right|}^{2}}=16\]


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