We investigate the two-dimensional continuous size-based separation of suspended particles in gravity-driven deterministic lateral displacement (g-DLD) devices. The suspended particles are driven through a periodic array of cylindrical obstacles under the action of gravity. We perform experiments covering the entire range of forcing orientations with respect to the array of obstacles and identify specific forcing angles that would lead to vector separation, in which different particles migrate, on an average, in different directions. A simple model, based on the lateral displacement induced on the trajectory of a particle by irreversible particle-obstacle interactions, accurately predicts the dependence of the migration angle on the forcing direction. The results provide design guidance for the development of g-DLD devices. We observe directional locking, which strongly depends on the size of the particle and suggests that relatively small forcing angles are well suited for size-fractionation purposes. We demonstrate excellent separation resolution for a binary mixture of particles at relatively small forcing angles, that is, forcing angles that are close to but smaller than the first transition angle of the larger particles in the mixture.