A) \[0\]
B) \[[\overrightarrow{a}\,\,\overrightarrow{b}\,\,\overrightarrow{c}]\]
C) \[2\overrightarrow{a}\]
D) \[\overrightarrow{a}\]
E) none of these
Correct Answer: A
Solution :
\[\overrightarrow{a}.[(\overrightarrow{b}\times \overrightarrow{c})\times (\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c})]\] \[=\overrightarrow{a}.[\overrightarrow{b}\times \overrightarrow{c}\times \overrightarrow{a}+\overrightarrow{b}\times \overrightarrow{c}\times \overrightarrow{b}+\overrightarrow{b}\times \overrightarrow{c}\times \overrightarrow{c}]\] \[=\overrightarrow{a}.[\overrightarrow{b}\times \overrightarrow{c}\times \overrightarrow{a}]=0\]
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