1. How to calculate a dot product
A dot product is the multiplication of two vectors to form a scalar.
There are two ways to calculate the dot product.
where θ is the angle between A and B
Component of A along B A θ B

2. Examples of Dot Products

3. Definition of Work
Work is defined as the amount of force acting over a distance.
The unit of work is either Joules (J) or electron-volts (eV) Dr F

4. Example of Work y Δw Δh1 x m Δh2
The following is an example of the work done by gravity on a mass. y Δw
Δh1 x m
Δh2

5. Example of Work F (N) 1 -1 A1 X (m) 1 2 A2
This is an example using the the fact that integrals are areas under a curve.
F (N) 1 -1 A1
X (m) 1 2 A2