In this paper a unified framework for vectorial parametrisation of inertia, Coriolis and centrifugal, and hydrodynamic added mass forces for marine vehicles in 6 degrees of freedom (DOF) is presented. Emphasises is placed on representing the 6 DOF nonlinear marine vehicle equations of motion in vector form satisfying certain matrix properties like symmetry, skew-symmetry and positive definiteness. For marine vehicles, this problem was first addresed by Fossen [1]. The proposed representations in this paper are based on extensions of this work. The main results are presented as two theorems. The first theorem is derived by applying Newton's equations whereas the second theorem reviews the main results of Sagatun and Fossen [6] where the Lagrangian formalism is applied.