Plotting and visualizing a 3D plot of a vector function

In summary, the conversation is about trying to figure out how to plot a certain vector valued function. The function is r(u,v) = <u + v, 3 - v, 1 + 4u + 5v> and the speaker has tried making a table with some u and v values to visualize the function, but it got too confusing. They then discuss the idea of creating a loop for u and v to get different (r,u) values, but the speaker is still struggling to visualize the function as a plane in 3D space. Another person suggests taking three points to determine the plane and plot it that way. The speaker agrees and suggests doing it on paper.
  • #1
Thales Costa
12
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
 
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  • #2
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).
 
  • #3
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.
 
  • #4
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.
 
  • #5
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


?
 

1. What is a vector function?

A vector function is a mathematical function that takes one or more inputs and outputs a vector, which is a quantity that has both magnitude and direction. It is often represented by a set of equations or parametric equations.

2. How do you plot a 3D graph of a vector function?

To plot a 3D graph of a vector function, you will need to first determine the domain and range of the function. Then, use a graphing software or manually plot points by substituting different values for the input variables and plotting the resulting vectors in a 3D coordinate system.

3. What is the purpose of visualizing a 3D plot of a vector function?

Visualizing a 3D plot of a vector function allows us to better understand the behavior of the function and how it changes with different input values. It can also help us identify any patterns or relationships between the input and output variables.

4. How can I interpret a 3D graph of a vector function?

A 3D graph of a vector function can be interpreted by looking at the shape and direction of the plotted vectors. The magnitude of the vector represents the value of the function at that point, while the direction represents the direction of change.

5. Are there any tools or techniques for enhancing the visualization of a 3D plot of a vector function?

Yes, there are various tools and techniques that can help enhance the visualization of a 3D plot of a vector function. This includes using different color schemes, adding labels and legends, and adjusting the scale and perspective of the graph. Additionally, using interactive graphing software allows for more dynamic and customizable visualizations.

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