Consider a particle moves from one point A to another point A’ due to an external force F as shown in Fig. 9.1

Here,

Vector AA’ = dr = Displacement of particle

Position vector of A is Vector r

Position vector of A’ is Vector r + dr

Then,

Work, du can be given by-

du = F . dr

i.e.,

Magnitude of work is the product of force and displacement.

|F| = F and |dr| = ds

For dot product, it can be written as-

du = F ds cos

where,

= Angle between F and d

It defines the magnitude of work is the product of component of force and displacement. The component of force should be in the direction of displacement.