Mathematics - Vector Question with Solution | TestHub

$\vec{a}+\vec{b}+\vec{c}=0\Rightarrow (\vec{a}+\vec{b}+\vec{c})\cdot (\vec{a}+\vec{b}+\vec{c})=0$ $|\vec{a}{|}^2+|\vec{b}{|}^2+|\vec{c}{|}^2+2(\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a})=0$ $\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a}=\frac{-1-4-9}{2}=-7$