A) \[(a\times a\,)\,.\,(b\times a)\]
B) \[a\,.\,(b\times a)-b\,.\,(a\times b)\]
C) \[[a\,.\,(a\times b)]\,a\]
D) \[(a\,.\,a)\,(b\times a)\]
Correct Answer: D
Solution :
\[\mathbf{a}\times [\mathbf{a}\times (\mathbf{a}\times \mathbf{b})]=\mathbf{a}\times \{(\mathbf{a}\,.\,\mathbf{b})\,\mathbf{a}-(\mathbf{a}\,.\,\mathbf{a})\mathbf{b}\}\] \[=(\mathbf{a}\,.\,\mathbf{b})(\mathbf{a}\times \mathbf{a})-(\mathbf{a}\,.\,\mathbf{a})(\mathbf{a}\times \mathbf{b})\]\[=(\mathbf{a}\,.\,\mathbf{b})\,0+(\mathbf{a}\,.\,\mathbf{a})(\mathbf{b}\times \mathbf{a})\] \[=(\mathbf{a}\,.\,\mathbf{a})\,\,(\mathbf{b}\times \mathbf{a})\].
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