## Kuvaus

## eMath 5: Vectors

- 300-400 assignments + answers, in three levels of complexity
- Numerous example solutions
- Possibility to add comments and highlight text
- Possibility to check the correctness of the calculation

**Overview:** The book gives an overview of vectors and vector spaces. It explains the basic notion of a vector, how to compute with vectors and how to describe them in a coordinate system. Three-dimensional vectors are also described, together with planes and lines in space.

### Table of contents:

** 1 Preface**

**2 The Vector Concept**

2.1 Vectors

**3 Arithmetic Rules for Vectors**

3.1 Vector Addition and Subtraction

3.2 Multiplying a Vector by a Number

3.3 Dot Product

**4 Vectors in Coordinate Systems**

4.1 Position Vectors

4.2 Vector Decomposition

4.3 Base Vectors i and j

4.4 The Direction Vector of a Line

4.5 The Normal Vector of a Line

4.6 The Proportionality Vector

**5 Vectors in Space**

5.1 Vectors in Three Dimensions

5.2 Addition and Subtraction

5.3 Dot Product

5.4 The Length of a Vector

**6 The Plane**

6.1 Definition of a Plane

6.2 Normals to a Plane

6.3 The Equation of a Plane

**7 Lines in Space**

7.1 The Equation of a Line in an xyz -Coordinate System

7.2 The Symmetric Equations of a Line

7.3 A Line and a Plane