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:
  1. point-normal form
  2. standard form
  3. vector form
  4. 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