Surface created by 1 plane equation

[riemannsigma]

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

 

[SteamKing]

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.

 

[chiro]

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.