## Abstract

**Vector algebras**^{1} is the algebra of vectors: a set of mathematical rules that allows meaningful and useful operations in the study of electromagnetics. We will define vectors and the necessary operations shortly, but, for now, it is useful to remember the following axiom which will be followed throughout this book: Nothing will be defined, no quantity or operation will be used, unless it has some utility either in explaining the observed physical quantities or otherwise simplifies the discussion of a topic. This is important because, as we increase our understanding of the subject, topics may seem to be disconnected, particularly in this and the following chapter. The discussion of vector algebra and vector calculus will be developed separately from the ideas of the electromagnetic field but for the purpose of describing the electromagnetic field. It is also implicit in this statement that by doing so, we should be able to simplify the discussion of electromagnetics and, necessarily, better understand the physical properties of fields.

## Keywords

Vector Field Unit Vector Scalar Product Scalar Field Position Vector## Preview

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