A) \[{{[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]}^{2}}\]
B) \[[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]\]
C) \[2[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]\]
D) \[3[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]\]
E) \[[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]\]
Correct Answer: B
Solution :
\[\therefore \] \[[\overrightarrow{a}\overrightarrow{a}+\overrightarrow{b}\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}]\] \[=(\overrightarrow{a}\times (\overrightarrow{a}+\overrightarrow{b})).(\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c})\] \[=(\overrightarrow{a}\times \overrightarrow{b})(\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c})=(\overrightarrow{a}\times \overrightarrow{b}).\overrightarrow{c}=[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}]\]
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