Let a, b, c be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and ( a ×…

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