In classical hydrodynamics with uniform density, vortices move with the local fluid velocity. This description is rewritten in terms of forces arising from the interactions with other vortices. For example, two positive vortices experience a repulsive interaction and precess in the positive (anti-clockwise) sense. In contrast, coherent rf Rabi coupling between two components of a Bose-Einstein condensate (BEC) acts very differently: for two positive vortices, one in each component, the Rabi coupling induces an attractive interaction. As a result, the positive vortices now precess in the negative (clockwise) sense. In addition, coherent rf Rabi coupling with a single vortex in a two-component trapped BEC induces periodic transfer of vorticity between the two components at the applied Rabi frequency.