Mathematics - Vector Question with Solution | TestHub

We have, $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\Rightarrow (\vec{a}+\vec{b}+\vec{c}{)}^2=0$ $\Rightarrow |\vec{a}{|}^2+|\vec{b}{|}^2+|\vec{c}{|}^2+2(\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a})=0\Rightarrow 25+16+9+2(\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a})=0$ $\Rightarrow (\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a})=-25\therefore |\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a}|=25$