Scalar product means dot product and dot product of 2 vectors gives a scalar , example dot product of force and displacement gives work which is scalar

The scalar product of two vectors can be constructed by taking the component of one vector in the direction of the other and multiplying it times the magnitude of the other vector. This can be expressed in the form

A = Ax i+ Ay j+ Azk

B = Bx i+ By j+ Bzk

A. B = (Ax i+ Ay j+ Azk). ( Bx i+ By j+ Bzk)

A. B = AxBx + AyBy + AzBz

Scalar product is

a) Commutative:

b) Distributive

if a body of mass m move with velocity u under the action of force F. Its velocity become v after displaced by s. then v2=u2+2as v2−u2=2as mv2−mu2=2mas 12mv2−12mu2=Fs Kf−Ki=W ΔK=W

Work done is given by

W = (Fcos)d

here Fcos is the component of applied force in direction of displacement and d is magnitude of displacement.

Work done = force in the direction of displacement multiplied by displacement

Work done is given as

W = Fdcos

Here is the angle between F and d if both are perpendicular then = 90 degree so cos = 0 and thus work done is 0 .

In International System of Units (SI) the newton is the unit for force. It is equal to the amount of net force required to accelerate a mass of one kilogram at a rate of 1 m/sec2 in direction of the applied force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion.

Dyne is a cgs unit of force. One dyne is equal to 10−5 N

Work done by a variable force is given by W = ∫F(x)dx above integration gives us area area under F and x.