We report on the degree of order of the vortex solid in YBa2Cu3O7 single crystals observed in ac susceptibility measurements. We show that when vortices are shaken by a temporarily symmetric ac field they are driven into an easy-to-move, ordered structure but, on the contrary, when the ac field is temporarily asymmetric, they are driven into a more pinned disordered state. This is characteristic of tearing of the vortex lattice and shows that ordering due to symmetric ac fields is essentially different from an equilibration process or a dynamical crystallization that is expected to occur at high driving currents.