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JEE Main & Advanced Mathematics Vector Algebra Question Bank Vector or Cross product of two vectors and its application

  • question_answer
    If \[\mathbf{a}=2\mathbf{i}-3\,\mathbf{j}-\mathbf{k}\] and \[\mathbf{b}=\mathbf{i}+4\mathbf{j}-2\mathbf{k}\], then \[\mathbf{a}\times \mathbf{b}\] is [MP PET 2001]

    A)                 10i + 2j + 11k

    B)                 10i + 3j + 11k

    C)                 10i ? 3j + 11k

    D)                 10i ? 3j ? 10k

    Correct Answer: B

    Solution :

               \[\mathbf{a}\times \mathbf{b}=\left| \,\begin{matrix}    \mathbf{i} & \mathbf{j} & \mathbf{k}  \\    2 & -3 & -1  \\    1 & 4 & -2  \\ \end{matrix}\, \right|\]\[=\mathbf{i}(6+4)-\mathbf{j}\,(-4+1)+\mathbf{k}(8+3)\]                                         \[=10\mathbf{i}+3\mathbf{j}+11\mathbf{k}.\]


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