NOTE TO SELF: SW: initially this chapter had a very mathematical approach. I have toned this down and tried to present in a logical way the techniques of vector manipulation after first exploring the mathematical properties of vectors. Most of the PGCE comments revolved around the omission of the graphical techniques of vector addition (i.e. scale diagrams), incline questions and equilibrium of forces. I have addressed the first two equilibrium of forces and the triangle law of three forces in equilibrium I think would be better off in the Forces Chapter. Also the Forces chapter should include some examples of incline planes. Inclines are introduced here merely as an example of components in action!