A) \[|\mathbf{a}{{|}^{2}}\mathbf{b}\]
B) \[|\mathbf{a}{{|}^{3}}\mathbf{b}\]
C) \[|\mathbf{a}{{|}^{4}}\mathbf{b}\]
D) None of these
Correct Answer: C
Solution :
\[\mathbf{a}\times [\mathbf{a}\times \{\mathbf{a}\times (\mathbf{a}\times \mathbf{b})\}]=\mathbf{a}\times [\mathbf{a}\times \{\mathbf{a}\times ab\,\mathbf{\hat{n}}\}]\] \[=\mathbf{a}\times [\mathbf{a}\times {{a}^{2}}\mathbf{b}]=\mathbf{a}\times {{a}^{3}}b\,\mathbf{\hat{n}}=|\mathbf{a}{{|}^{4}}\mathbf{b}.\]
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