How to Convert a Plane from Coordinate Form to Parametric Form

Introduction

A plane equation is a representation of a flat plane in a three-dimensional coordinate system. Converting a plane equation from coordinate form to parametric form involves three steps.

Step 1: Solve the Plane Equation for x₃

Solve the plane equation for x₃ to get an equation in the form x₃ = f(x₁, x₂).

Step 2: Parameterize the Plane Equation

Introduce two parameters, say s and t, and rewrite the equation obtained in Step 1 as:

``` x<sub>1</sub> = x<sub>1</sub>(s, t) x<sub>2</sub> = x<sub>2</sub>(s, t) x<sub>3</sub> = f(x<sub>1</sub>(s, t), x<sub>2</sub>(s, t)) ```

Step 3: Express Parameters in Terms of s and t

Determine the equations for s and t in terms of x₁ and x₂. These equations will provide the parametric representation of the plane.