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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 \[|\mathbf{a}|\,=2,\,\,|\mathbf{b}|\,=3\] and a, b are mutually perpendicular, then the area of the triangle whose vertices are \[\mathbf{0},\,\,\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] is

    A)                 5

    B)                 1

    C)                 6

    D)                 8

    Correct Answer: C

    Solution :

               Let the position vectors of the points \[A,\,\,B,\,\,C\] are 0, \[\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] and \[\theta =90{}^\circ .\]            Area of triangle \[=\frac{1}{2}|\overrightarrow{AB}\times \overrightarrow{AC}|\]                                \[=\frac{1}{2}|(\mathbf{a}+\mathbf{b})\times (\mathbf{a}-\mathbf{b})|=\frac{1}{2}|2\mathbf{b}\times \mathbf{a}|\]                                             \[=ba\sin \theta =3\times 2\sin 90{}^\circ =6.\]


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