If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three unit vectors satisfying \(|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\ve…

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three unit vectors satisfying \(|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2=9\), then \(|3 \vec{a}+3 \vec{b}+8 \vec{c}|\) equals