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JEE Main & Advanced Mathematics Vector Algebra Question Bank Scalar triple product and their applications

  • question_answer
    Given vectors a, b, c such that \[\mathbf{a}\,.(\mathbf{b}\times \mathbf{c})\]\[=\lambda \ne 0,\,\] the value of \[(\mathbf{b}\times \mathbf{c})\,.\,(\mathbf{a}+\mathbf{b}+\mathbf{c})/\lambda \]  is                            [AMU 1999]

    A)             3         

    B)             1

    C)             \[-3\lambda \]

    D)             \[3/\lambda \]

    Correct Answer: B

    Solution :

                    \[\frac{(b\times c)\,.\,(a+b+c)}{\lambda }\]\[=\frac{(b\times c)\,.\,a+(b\times c)\,.\,b+(b\times c)\,.\,c}{\lambda }\]                 \[=\frac{(b\times c)\,.\,a+0+0}{\lambda }\]\[=\frac{\lambda }{\lambda }=1\],  (\[\because \]Given\[a\,.\,(b\times c)=\lambda =(b\times c)\,.\,a\]).


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