A) \[\sqrt{12}\]
B) \[2\sqrt{12}\]
C) \[3\sqrt{14}\]
D) \[3\sqrt{12}\]
E) \[2\sqrt{14}\]
Correct Answer: E
Solution :
\[\overrightarrow{a}=\hat{i}+2\hat{j}+3\hat{k}\]and \[\overrightarrow{b}=\hat{i}\times (\overrightarrow{a}\times \hat{i})+\hat{j}\times (\overrightarrow{a}\times \hat{j})+\hat{k}\times (\overrightarrow{a}\times \hat{k})\] \[=3\overrightarrow{a}-\overrightarrow{a}=2\overrightarrow{a}\] \[=2(\hat{i}+2\hat{j}+3\hat{k})\] \[\Rightarrow \] \[|\overrightarrow{b}|=\sqrt{4+16+36}\] \[=\sqrt{56}\] \[=2\sqrt{14}\]
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