Plotting and visualizing a 3D plot of a vector function

[Thales Costa]

Hello, I'm trying to figure out how to plot a certain vector valued function but I'm having a hard time.

The problem gives me the following vector valued function:

r(u,v) = <u + v, 3 - v, 1 + 4u + 5v>​

I don't know how to plot this. So far I've tried making a table with some u and v values to get the x, y and z values so I can plot it, but it got too confusing.

Thanks in advance

 

[erbilsilik]

Where did you try it? I think you can do it by starting to giving the same value to u and v. You can try to create a loop for u and v then for each value there will be different (r,u).

 

[Thales Costa]

Where did you try it? I think you can do it by starting to giving the same value to u and v. You can try to create a loop for u and v then for each value there will be different (r,u).

Trying on paper.

Got this table. The values of Z get too high after increasing u and v by a bit. I know the surface will be a plane, but I can't visualize it in a 3D space.

 

[micromass]

You know it will be a plane. Any plane is determined by three points. So just take three points, plot them and the plane through it is the one you're looking for.

 

[Thales Costa]

You know it will be a plane. Any plane is determined by three points. So just take three points, plot them and the plane through it is the one you're looking for.

So, like this:

?