A) \[a\]
B) \[\sqrt{2}a\]
C) \[\sqrt{3}a\]
D) \[2\,a\]
E) none of these
Correct Answer: C
Solution :
\[|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}{{|}^{2}}=|\overrightarrow{a}{{|}^{2}}+|\overrightarrow{b}{{|}^{2}}+|\overrightarrow{c}{{|}^{2}}\] \[+2(\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a})\] \[={{a}^{2}}+{{a}^{2}}+{{a}^{2}}\] (\[\because \]\[\overrightarrow{a},\overrightarrow{b}\]and\[\overrightarrow{c}\]are mutually perpendicular) \[\Rightarrow \] \[|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=\sqrt{3}a\]
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