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

  • question_answer
    The area of the parallelogram whose adjacent sides are \[\mathbf{i}-\mathbf{k}\] and \[2\mathbf{j}+3\mathbf{k}\] is                                       [UPSEAT 2004]

    A)                 2

    B)                 4

    C)                 \[\sqrt{17}\]

    D)                 \[2\sqrt{13}\]

    Correct Answer: C

    Solution :

               Area of parallelogram \[=\text{ }|\mathbf{a}\times \mathbf{b}|\text{ }=\left| \,\left| \begin{matrix}    \mathbf{i} & \mathbf{j} & \mathbf{k}  \\    1 & 0 & -1  \\    0 & 2 & 3  \\ \end{matrix} \right|\, \right|\]                                 \[=\,|2\mathbf{i}-3\mathbf{j}+2\mathbf{k}|\]\[=\sqrt{4+9+4}=\sqrt{17}\].


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