This chapter is of a preliminary nature and is designed to indicate the level of knowledge assumed in the development of the third and subsequent chapters. It deals with those elementary properties of vectors and their algebra which will be used later. The results and properties are usually stated without proof, but with illustrations, and a set of exercises is included at the end in section 2.10 to enable the student to decide whether or not further preliminary study is needed. It is suggested that the reader who already has some working familiarity with vector algebra might first attempt the exercises and return to this chapter only if he has difficulty with them.

Definitions

The simplest kind of physical quantity is one which can be completely specified by its magnitude, a single number together with the units in which it is measured. Such a quantity is called a scalar and examples include temperature, time, work, and [scalar] potential.

Quantities which require both a magnitude (≥ 0) and a direction in space| to specify them are known (with a few exceptions, such as finite rotations, discussed below) as vectors; familiar examples include position with respect to a fixed origin, force, linear momentum and electric field. Using an arbitrary but generally accepted convention, vectors can be used to represent angular velocities and momenta, the axis of rotation being taken as the direction of the vector and the sense being such that the rotation appears clockwise when viewed parallel [as opposed to antiparallel] to the vector.