In Chapter 1 we observed that positions and velocities of particles are specified by indicating their unit, magnitude and directions. Hence, they are vectors. In the present chapter we learn how vectors are defined in mathematics, and how they are used and handled in physics. In order to provide a formal definition we introduce a number of mathematical concepts, like groups, that will be revisited in forthcoming chapters. As first important application we deal with balancing forces and torques.

At the end of this chapter we will be able to determine how a mobile hangs from the ceiling.

• 2.1 Motivation and outline: forces are vectors
• 2.2 Sets
• 2.3 Groups
• 2.4 Fields
• 2.5 Vector spaces
• 2.6. Physics application: balancing forces
• 2.7 The inner product
• 2.8 Cartesian coordinates
• 2.9 Cross products — torques
• 2.10 Worked example: Calder's mobiles
• 2.11 Problems
• 2.12 Further reading

The PDF file of the chapter is available here.