IMS Content
1.1.4
M208_1_1.0
Vectors and conics
Attempts to answer problems in areas as diverse as science, technology and economics involve solving simultaneous linear equations. In this unit we look at some of the equations that represent points, lines and planes in mathematics. We explore concepts such as Euclidean space, vectors, dot products and conics.
Mathematics and Statistics
Algebra
Equations
Vectors
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An OU course on this topic  Open University links
URL
http://www3.open.ac.uk/courses/
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Study this topic at the OU  Open University links
URL
http://www3.open.ac.uk/courses/classifications/mathematics_and_statistics.shtm
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open2.net: Science & nature  Open University links
URL
http://www.open2.net/sciencetechnologynature/
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COURSE
Pure Mathematics  M208
Vectors and conics

Introduction

Introduction

1 Coordinate geometry: points, planes and lines

1.1 Points, lines and distances in twodimensional Euclidean space

1.2 Lines

1.3 Parallel and perpendicular lines

1.4 Intersection of two lines

1.5 Distance between two points in the plane

1.6 Points, planes, lines and distances in threedimensional Euclidean space

1.7 Planes in threedimensional Euclidean space

1.8 Intersection of two planes

1.9 Distance between points in threedimensional Euclidean space

1.10 Further exercises

2 Vectors

2.1 Definitions

2.2 Multiplication by a scalar

2.3 Addition of vectors

2.4 Components and the arithmetic of vectors

2.5 Position vectors

2.6 Lines

2.7 Further exercises

3 Dot product

3.1 Definition, properties and some applications

3.2 Postaudio exercises

3.3 Equation of a plane in threedimensional Euclidean space

3.4 Further exercises

4 Conics

4.1 Conic sections

4.2 Circles

4.3 Focus–directrix definitions of the nondegenerate conics

4.4 Parabola (e = 1)

4.5 Ellipse (0

4.6 Hyperbola (e > 1)

4.7 Rectangular hyperbola (e = √2)

4.8 General equation of a conic

4.9 Further exercises

References and Acknowledgements

Acknowledgements

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