Surface created by 1 plane equation

  • #1
I am having a difficult time seeing the three dimensional surface formed from a plane of equation 2x + y + z = 2 strictly inside the first quadrant.

On the 2 dimensional xy plane, the closed, simple, piece wise curve is C1 along the x axis from x=0 to 1, C2 along the line y= 2-2x is between x=0 to x=1 and y=0 to y=2, and C3 is along the y axis from y=0 to y=2.

Besides the boundary curve, it is very difficult for me to see the 3 dimensional Surface bounded by this curve.

HELP
 

Answers and Replies

  • #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,796
1,668
I am having a difficult time seeing the three dimensional surface formed from a plane of equation 2x + y + z = 2 strictly inside the first quadrant.

On the 2 dimensional xy plane, the closed, simple, piece wise curve is C1 along the x axis from x=0 to 1, C2 along the line y= 2-2x is between x=0 to x=1 and y=0 to y=2, and C3 is along the y axis from y=0 to y=2.

Besides the boundary curve, it is very difficult for me to see the 3 dimensional Surface bounded by this curve.

HELP
You have a first order equation in the variables x, y, and z. What simple surface comes to mind? Remember, the intersection of this surface with the x-y, y-z, and x-z planes is a straight line.
 
  • #3
chiro
Science Advisor
4,790
132
Hey riemannsigma.

I would advise you first to find the solution to these two constraints algebraically and then classify the solution based on geometric primitives.

Flat planes have a very specific form in the way of <n,r-r0> = 0 where r0 is a point on the plane, n is the normal vector and r is a general point.

Other shapes include things like a sphere, torus, parabolic surface and others.

You can - if you get stuck, use a computer algebra and plotting program to plot the regions and visualize them (if they are three dimensions or lower).

This is quite common and it will help visualize things that may not be easy to do algebraically.
 

Related Threads on Surface created by 1 plane equation

Replies
1
Views
2K
Replies
16
Views
10K
Replies
1
Views
15K
Replies
5
Views
3K
  • Last Post
Replies
1
Views
2K
Replies
3
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
Replies
7
Views
2K
Top