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eMath 5: Vectors

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The ebooks are structured so that you will learn all concepts in a logical order and it is meant to be studied from beginning to end. The theory parts are short and concise and at the end of each lesson, you will find a page with assignments. The assignments can be solved directly in the book.
You can easily write mathematics on the computer with the 4f Studio math tools, as well as insert pictures, embedded elements and graphs to support your studies and solutions. When your are finished, you can let the computer automatically check your assignments. The automatic checker sends each step in the derivation to an automatic theorem prover. If each step in the derivation is proved correct, the derivation is correct. The checker warns when it was not able to prove a derivation step correct, so that you can inspect the step, see your mistakes easily and correct them. See 4f Checker for more details.
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  • Numerical and symbolical calculator

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