A) \[\frac{19}{2}\]
B) \[-\frac{19}{2}\]
C) \[\frac{29}{2}\]
D) \[-\frac{29}{2}\]
Correct Answer: D
Solution :
Given, \[\vec{a}+\vec{b}+\vec{c}=0\] \[\Rightarrow \]\[{{(\vec{a}+\vec{b}+\vec{c})}^{2}}=0\] \[\Rightarrow \]\[|\vec{a}{{|}^{2}}+|\vec{b}{{|}^{2}}+|\vec{c}{{|}^{2}}\] \[+\,2(\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a})=0\] \[\Rightarrow \]\[4+9+16+2(\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a})=0\] \[\Rightarrow \]\[\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}=\frac{-29}{2}\]
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