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Describe and sketch the surface in $ \mathbb{R}^3 $ represented by the equation $ x + y = 2 $.

The graph is a vertical plane that intersects the $x y-$

plane along the line $x+y=2 .$ Remember that

planes are infinite, so the sketch only represents a

portion of the plane.

Vectors

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Kyle P.

May 11, 2020

you didnt explain anything. why are we plotting z

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

All right. So we're trying to describe and sketch the surface X plus Y equals two in our three. So um we're very good at describing expose valuables to in our too. So let's just do that first. Um this is a line in our two. Uh it has slope negative one. Let's just write it as what it calls negative X plus two so that everyone's comfortable. Um Why intercept to slope negative 1? So there's that line. Um Now in our three we usually introduces Z, but there's no Z here. And actually in math, that just means he can be anything. So we have this line X plus Y equals two and now Z can be anything in the xy plane 00 So if we go up to three dimensions, I like to draw my coordinate axes like this, but you can draw them anyway that it follows the right hand rule. Um So we have this line. Yeah, sorry about that. I'm going to draw this. This is that same line, right? It's just in a different perspective. There's two zero. This other intercept actually is also to and then Z can be anything. So this actually comes up and down and it's like a vertical wall. So this is a vertical surface, it's perpendicular to the xy plane, It's at a 45 degree to both the X. And Y axis, just like that line was. Um And that is the surface.

University of Washington

Vectors