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