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 .