### Introduction

In engineering, frequent reference is made to physical quantities, such as force, speed and time. For example, we talk of the speed of a car, and the force in a compressed spring. It is useful to separate these physical quantities into two types. Quantities of the first type are known as
**
scalars
**
. These can be fully described by a single number known as the
**
magnitude
**
. Quantities of the second type are those which require the specification of a
**
direction
**
, in addition to a magnitude, before they are completely described. These are known as
**
vectors
**
. Special methods have been developed for handling vectors in calculations, giving rise to subjects such as vector algebra, vector geometry and vector calculus. Quantities that are vectors must be manipulated according to certain rules, which are described in this and subsequent Sections.

#### Prerequisites

- be familiar with all the basic rules of algebra

#### Learning Outcomes

- categorize a number of common physical quantities as scalar or vector
- represent vectors by directed line segments
- combine, or add, vectors using the triangle law
- resolve a vector into two perpendicular components

#### Contents

1 Introduction2 The mathematical description of vector quantities

3 Addition of vectors

3.1 Example: The route taken by an automated vehicle

3.2 Example: Resultant of two forces acting upon a body

3.3 Example: Resolving a force into two perpendicular directions

3.4 The force vectors on an aeroplane in steady flight

4 Subtraction of vectors

5 Multiplying a vector by a scalar

5.1 Unit vectors