A) 47
B) \[-47\]
C) 0
D) 25
E) \[-25\]
Correct Answer: E
Solution :
\[\because \] \[u+v+w=0\] \[\therefore \] \[|\overrightarrow{u}{{|}^{2}}+|\overrightarrow{v}{{|}^{2}}+|\overrightarrow{w}{{|}^{2}}+2(\overrightarrow{u}.\overrightarrow{v}+\overrightarrow{v}.\overrightarrow{w}\]\[+\overrightarrow{w}.\overrightarrow{u})=0\] \[\Rightarrow \]\[9+16+25+2(\overrightarrow{u}.\overrightarrow{v}+\overrightarrow{v}.\overrightarrow{w}+\overrightarrow{w}.\overrightarrow{u})=0\] \[\Rightarrow \]\[\overrightarrow{u}.\overrightarrow{v}+\overrightarrow{v}.\overrightarrow{w}+\overrightarrow{w}.\overrightarrow{u}=-25\]
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