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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 the vectors \[\mathbf{a},\,\mathbf{b}\] and c are represented by the sides \[BC,\,CA\] and \[AB\] respectively of the \[\Delta ABC\], then [IIT Screening 2000]

    A)                 \[\mathbf{a}\,\mathbf{.}\,\mathbf{b}+\mathbf{b}\,\mathbf{.}\,\mathbf{c}+\mathbf{c}\,\mathbf{.}\,\mathbf{a}=0\]

    B)                 \[\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}=\mathbf{c}\times \mathbf{a}\]

    C)                 \[\mathbf{a}\,\mathbf{.}\,\mathbf{b}=\mathbf{b}\,\mathbf{.}\,\mathbf{c}=\mathbf{c}\,\mathbf{.}\,\mathbf{a}\]

    D)                 \[\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}=\mathbf{c}\times \mathbf{a}=0\]

    Correct Answer: B

    Solution :

                    Here \[a+b+c=0\]. Take cross products with a and b by turn.


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