How to Parameterize a Plane Between Two Given Planes

[ƒ(x)]

Homework Statement

Find parametric equations for the portion of the plane x+y = 1 that extends between the planes z = -1 and z = 1

The attempt at a solution

z = u -1$$\leq$$u$$\leq$$1

x = ?
y = ?

 

[Mark44]

Can you write x + y = 1 in parametric form? I.e., x = an expression in t (the parameter), y = another expression in t.

For z, all you need is -1 $\leq$ z $\leq$ 1. No parameter needed.

 

[ƒ(x)]

What do you mean?

I can have x and y equal anything as long as they both add up to 1

 

[ƒ(x)]

Like if I made x = 3t + t^2, then y = 1 - 3t - t^2

 

[Mark44]

Why not let x = t? Why would you pick x = 3t + t^2?

 

[LCKurtz]

To parameterize a surface you need two parameters. They can't be x and y in this problem because one of them determines the other. So try perhaps x and z as your parameters.

R(x,z) = < ?, ?, ?>

where you express the x, y, and z components in terms of x and z. It's really easy...