A) 16
B) 64
C) 4
D) 8
Correct Answer: A
Solution :
\[[\mathbf{a}\times \mathbf{b}\,\,\mathbf{b}\,\times \mathbf{c}\,\,\mathbf{c}\times \mathbf{a}]=(\mathbf{a}\times \mathbf{b})\,.\,[(\mathbf{b}\times \mathbf{c})\times (\mathbf{c}\times \mathbf{a})]\] \[=(\mathbf{a}\times \mathbf{b})\,.\,(\,[\mathbf{b}\,\mathbf{c}\,\mathbf{a}]\,\mathbf{c}-[\mathbf{b}\,\mathbf{c}\,\mathbf{c}]\,\mathbf{a})\]\[=(\mathbf{a}\times \mathbf{b})\,.\,(\,[\mathbf{b}\,\mathbf{c}\,\mathbf{a}]\,\mathbf{c}-0)\] \[=[\mathbf{b}\,\mathbf{c}\,\mathbf{a}]\,[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]=[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]\,[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]=4.4=16.\]
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