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Introduction

This unit introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the unit assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian coordinates for specifying a point in a plane.

Learning Outcomes

After studying this unit you should:

know some basic definitions and terminology associated with scalars and vectors and how to represent vectors in two dimensions;
understand how vectors can be represented in three (or more) dimensions and know both plane polar and Cartesian representations;
know ways to operate on and combine vectors.

Using vectors to model

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.

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Click 'View document' to open the answer book (PDF, 0.4 MB).

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Workbook contents

Introduction

1 Describing and representing vectors

1.1 Scalars and vectors

1.2 Vector notation

1.3 Using arrows to represent vectors

1.4 Equality of vectors

1.5 Polar representation of two-dimensional vectors

2 Scaling and adding vectos

2.1 Scaling a vector

2.2 Addition of vectors

2.3 Algebraic rules for scaling and adding vectors

3 Cartesian components of a vector

3.1 Vectors in two dimensions

3.2 Vectors in three dimensions

4 Products of vectors

4.1 The dot product

4.2 The cross product

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Acknowledgements

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

All materials included in this unit are derived from content originated at the Open University.

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Fri, 01 Aug 2008 08:45:52 GMT

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