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
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