A) \[\overrightarrow{0}\]
B) \[\overrightarrow{a}\]
C) \[2\overrightarrow{a}\]
D) \[3\overrightarrow{a}\]
E) \[4\overrightarrow{a}\]
Correct Answer: C
Solution :
\[\hat{i}\times (\overrightarrow{a}\times \hat{i})+\hat{j}\times (\overrightarrow{a}\times \hat{j})+\hat{k}(\overrightarrow{a}\times \hat{k})\] \[=(\hat{i}.\hat{i})\overrightarrow{a}-(\hat{i}.\overrightarrow{a})\hat{i}+(\hat{j}.\hat{j})\overrightarrow{a}-(\hat{j}.\overrightarrow{a})\hat{j}\] \[+(\hat{k}.\hat{k})\overrightarrow{a}-(\hat{k}.\overrightarrow{a})\hat{k}\] \[=3\overrightarrow{a}-\overrightarrow{a}=2\overrightarrow{a}\]
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