A) \[5\sqrt{2}\]
B) \[\frac{5}{\sqrt{2}}\]
C) \[10\sqrt{2}\]
D) \[10\sqrt{3}\]
E) \[5\sqrt{3}\]
Correct Answer: A
Solution :
Given that \[\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})=0\] \[\Rightarrow \] \[\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{c}.\overrightarrow{a}=0\] Similarly,\[\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{a}.\overrightarrow{b}=0\]and \[\overrightarrow{c}.\overrightarrow{a}+\overrightarrow{b}.\overrightarrow{c}=0\] \[\therefore \] \[\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}=0\] Now, \[|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}{{|}^{2}}=|\overrightarrow{a}{{|}^{2}}+|\overrightarrow{b}{{|}^{2}}+|\overrightarrow{c}{{|}^{2}}\] \[+2(\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a})\]
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