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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 \[|\mathbf{a}|\,=2,\,\,|\mathbf{b}|\,=5\] and \[|\mathbf{a}\times \mathbf{b}|\,=8,\] then a . b is equal to                 [AI CBSE 1984; RPET 1991]

    A)                 0

    B)                 2

    C)                 4

    D)                 6

    Correct Answer: D

    Solution :

               \[\mathbf{a}\,.\,\mathbf{b}=\,|\mathbf{a}|\,|\mathbf{b}|\cos \theta \]; But \[|\mathbf{a}\times \mathbf{b}|\,=\,|\mathbf{a}|\,|\mathbf{b}|\,\sin \theta \]            \[\Rightarrow \sin \theta =\frac{|\mathbf{a}\times \mathbf{b}|}{|\mathbf{a}|\,|\mathbf{b}|}=\frac{4}{5}\Rightarrow \cos \theta =\frac{3}{5}\]                                 Therefore, \[\mathbf{a}\,.\,\mathbf{b}=2\times 5\times \frac{3}{5}=6.\]


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