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Foundation Mathematics for the Physical Sciences by K. F. Riley, M. P. Hobson

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9

Vector algebra

This chapter introduces space vectors and their manipulation. Firstly we deal with the description and algebra of vectors, then we consider how vectors may be used to describe lines, planes and spheres, and finally we look at the practical use of vectors in finding distances. The calculus of vectors will be developed in a later chapter; this chapter gives only some basic rules.

9.1  Scalars and vectors

The simplest kind of physical quantity is one that 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 and density.

A vector is a quantity that requires both a magnitude (≥0) and a direction in ...

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