The force between two current-carrying conductors acts at each point along the wire rather than solely along the center of mass. This localized force results from the magnetic fields generated by the currents in each conductor. To simplify analysis, the total force is often represented by a single vector, which is the sum of all the individual forces acting on the wire. This approach allows for easier calculations and understanding of the overall interaction. Ultimately, the representation of force as a single vector is a practical simplification of the more complex reality of distributed forces.