Let us consider a particle A which moves to A’ under the action of a force F. Vector AA = dr is the displacement of the particle (Fig. 9.1).

Vector r is the position vector of A

Vector r + dr is the position vector of A’

The work du is defined as the dot product between F an dr

du = f .dr

| f| = f

and | dr | = ds

By definition of dot product

du= F ds cos θ , … (9.2)

where e is the angle between F and d;. Thus, the magnitude of work is defined as the product of component of the force in the direction of displacement and the displacement.