A) \[{{\left| \,\overrightarrow{a}\, \right|}^{2}}\overrightarrow{b}\]
B) \[\left| \,\overrightarrow{a}\cdot \overrightarrow{b}\, \right|\,\overrightarrow{a}\]
C) \[\overrightarrow{a}\]
D) \[\overrightarrow{b}\]
Correct Answer: C
Solution :
\[(\vec{a}\cdot \vec{b})\,\vec{b}+\vec{b}\times (\vec{a}\times \vec{b})\] \[=(\vec{a}\cdot \vec{b})\,\vec{b}+(\vec{b}\cdot \vec{b})\,\vec{a}-(\vec{a}\cdot \vec{b})\,\vec{b}\] \[=\vec{a}\]
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