Mathematics

Problem

\vec{a}

\vec{b}

\vec{c}

are unit vectors such that

\vec{a}+\vec{b}+\vec{c}=\vec{0}

, find the value of

\vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{c}+\vec{c}\cdot\vec{a}

where

|\vec{a}|=|\vec{b}|=|\vec{c}|=1

and

\vec{a}+\vec{b}+\vec{c}=\vec{0}