A plane in 3-space can be thought of as "an
infinite flat surface". Of course, we can't draw a picture of something
infinite, so we usually represent a plane by drawing a small rectangular piece
of it. And since we'll rarely be looking at the plane "head on" in
3-space, we tilt the rectangle, making it look like a parallelogram, like
so:

A plane in 3-space can be represented by a single
scalar equation or in various other forms. In this learning object, we'll
look at different ways of representing planes in 3-space:

- point-normal form
- standard form
- vector form
- parametric form.

Then we'll look at some examples of how to find planes.

Prerequisites:
Basic vector geometry and algebra, including dot products. For the vector equation,
cross products and a little about linear systems and using augmented matrices to find their solutions.

Keywords:
point-normal equation of a plane, normal vector of a plane, standard equation
of a plane, vector equation of a plane, parametric equations of a plane

Using Vectors to Describe Planes | ||||

Introduction | The point-normal form of a plane | The standard equation of a plane | The vector equation of a plane | Finding planes |