Vectors and conics
Vectors and conics

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

Vectors and conics

Vectors and conics

Introduction

The idea of vectors and conics may be new to you. In this course we look at some of the ways that we represent points, lines and planes in mathematics.

In Section 1 we revise coordinate geometry in two-dimensional Euclidean space,2, and then extend these ideas to three-dimensional Euclidean space, 3. We discuss the equation of a plane in 3, but find that we do not have the tools to determine the equation of a plane, and leave this until Section 3.

In Section 2 we introduce the idea of a vector, and look at the algebra of vectors. Vectors give us a way of looking at points and lines, in the plane and in 3, which is sometimes more useful than Cartesian coordinates, although the two are closely related.

In Section 3 we introduce the idea of the dot product of two vectors, and then use it to determine the general form of the equation of a plane in 3.

In Section 4 we explain the origin of conics, as the curves of intersection of double cones and planes in 3. The focus–directrix definitions of the non-degenerate conics, the ellipse, the parabola and the hyperbola, are given. We observe that conics are precisely the subsets of the plane determined by an equation of degree two.

This OpenLearn course is an adapted extract from an Open University course M208 Pure Mathematics [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

M208_1

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to university level study, find out more about the types of qualifications we offer, including our entry level Access courses and Certificates.

Not ready for University study then browse over 900 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus