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I n t r o d u c t i o n
We use the words work, energy and power in our day-to-day life often.
Page 3


I n t r o d u c t i o n
We use the words work, energy and power in our day-to-day life often.
Work, Energy and Power
However, their meaning differ from the meaning we get from scientific
definitions.
Page 4


I n t r o d u c t i o n
We use the words work, energy and power in our day-to-day life often.
Work, Energy and Power
However, their meaning differ from the meaning we get from scientific
definitions.
The scalar product or dot product of any two vectors A and B, denoted as
A.B (Read A dot B) is defined as , where q is the angle between the two
vectors.
A, B and cos theta are scalars, the dot product of A and B is a scalar quantity.
Both vectors, A and B, have a direction but their scalar product does not
have a direction.
B is the product of the magnitude of A and the component of B along A.
Alternatively, it is the product of the magnitude of B and the component of A
along B.
Scalar Product
Page 5


I n t r o d u c t i o n
We use the words work, energy and power in our day-to-day life often.
Work, Energy and Power
However, their meaning differ from the meaning we get from scientific
definitions.
The scalar product or dot product of any two vectors A and B, denoted as
A.B (Read A dot B) is defined as , where q is the angle between the two
vectors.
A, B and cos theta are scalars, the dot product of A and B is a scalar quantity.
Both vectors, A and B, have a direction but their scalar product does not
have a direction.
B is the product of the magnitude of A and the component of B along A.
Alternatively, it is the product of the magnitude of B and the component of A
along B.
Scalar Product
Notions of Work and Kinetic Energy
The work-energy theorem states that the change in kinetic
energy of a particle is equal to the work done on it by the net
force.
Kf - Ki = W We know the equation in 3D: 
v² - u² = 2ad (where u = initial velocity, v = final velocity, a =
acceleration, d = displacement) 
Now multiplying the equation by m/2, we have: 
(1/2)mv² - (1/2)mu² = Fd (Since ma = F)
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