In a non-degenerate triangle $ABC$, let the lengths of the sides be $a, b, c$. Suppose the orthocenter $H$ satisfies the vector relation $\vec{OH} = \vec{OA} + \vec{OB} + \vec{OC}$, where $O$ is the circumcenter. If the triangle is defined by vertices $A(0, 4)$, $B(-3, 0)$, and $C(3, 0)$, which of the following is true regarding the distance from the circumcenter $O$ to the orthocenter $H$?