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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 triangle having vertices as  \[\mathbf{i}-2\mathbf{j}+3\mathbf{k},\] \[\,-2\mathbf{i}+3\mathbf{j}+\mathbf{k}\] , \[4\mathbf{i}-7\mathbf{j}+7\mathbf{k}\] is                     [MP PET 2004]

    A)                 26

    B)                 11

    C)                 36

    D)                 0

    Correct Answer: D

    Solution :

               Area of triangle \[\Delta =\frac{1}{2}|\overrightarrow{AB}\times \overrightarrow{AC}|\]                    \[\Delta =\frac{1}{2}\left| \,\left| \begin{matrix}    \mathbf{i} & \mathbf{j} & \mathbf{k}  \\    -2-1 & 3+2 & -1-3  \\    4-1 & -7+2 & 7-3  \\ \end{matrix}\, \right|\, \right|\]                                 \[\Delta =\frac{1}{2}\left| \,\left| \begin{matrix}    \mathbf{i} & \mathbf{j} & \mathbf{k}  \\    -3 & 5 & -4  \\    3 & -5 & 4  \\ \end{matrix}\, \right|\, \right|=0\].


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