Let $\vec{a},\vec{b},\vec{c}$ be three coplanar concurrent vectors such that the angles between any two of them are the same. If the product of their magnitudes is $14$ and $ (\vec{a}\times\vec{b})\cdot(\vec{b}\times\vec{c}) +(\vec{b}\times\vec{c})\cdot(\vec{c}\times\vec{a}) +(\vec{c}\times\vec{a})\cdot(\vec{a}\times\vec{b})=168, $ then $|\vec{a}|+|\vec{b}|+|\vec{c}|$ is equal to: