Consider a particle moves from one point A to another point A’ due to an external force F as shown in Fig. 9.1
Vector AA’ = dr = Displacement of particle
Position vector of A is Vector r
Position vector of A’ is Vector r + dr
Work, du can be given by-
du = F . dr
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
= 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.