Plotting and visualizing a 3D plot of a vector function

Click For Summary
SUMMARY

The discussion focuses on plotting the vector-valued function r(u,v) = . Participants suggest starting by assigning equal values to u and v, then creating a loop to generate corresponding (x, y, z) coordinates. It is confirmed that the surface represented by this function is a plane, which can be visualized by plotting three distinct points on the surface. This approach simplifies the visualization process in 3D space.

PREREQUISITES
  • Understanding of vector-valued functions
  • Familiarity with 3D coordinate systems
  • Basic programming skills for creating loops
  • Knowledge of plotting libraries (e.g., Matplotlib for Python)
NEXT STEPS
  • Learn how to use Matplotlib for 3D plotting in Python
  • Explore the concept of parametric surfaces in vector calculus
  • Study methods for visualizing mathematical functions in three dimensions
  • Investigate techniques for generating and plotting points in 3D space
USEFUL FOR

Mathematicians, educators, students in calculus or linear algebra, and anyone interested in visualizing vector functions in three-dimensional space.

Thales Costa
Messages
12
Reaction score
0
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
 
Physics news on Phys.org
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).
 
erbilsilik said:
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.

sRsftzG.png


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.
 
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.
 
micromass said:
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:
PFxYWGJ.jpg


?
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 17 ·
Replies
17
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
7
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 2 ·
Replies
2
Views
5K
Replies
2
Views
2K