The work done by a force is a scalar quantity equal to the product of the magnitude of the force and the resolved part of the displacement.
∴ F * S = dot products of force and displacement.
Suppose F1, F1,…, Fn are n forces acted on a particle, then during the displacement S of the particle, the separate forces do quantities of work F1 * S, F 2 * S, Fn * S.
Here, system of forces were replaced by its resultant R. Vector or Cross Product of Two Vectors The vector product of the vectors a and b is denoted by a * b and it is defined as
a * b =(| a | | b | sin θ) n = ab sin θ n …..( i)
where, a = | a |, b = | b |, θ is the angle between the vectors a and b and n is a unit vector which is perpendicular to both a and b, such that a, b and n form a right-handed triad of vectors.