Doubt in plotting Vector Fields

In summary, the conversation discusses the process of plotting a vector field and how it is done by marking the tail and head portions of the vector. There is some confusion about using (x,y) to represent both points and vectors, and it is suggested to use <x,y> or xi+ yj instead. The conversation also mentions a potential issue with online graphing software not handling zero vectors correctly.
  • #1
iamnotageek
5
0
Hi,

I have a doubt in plotting the vector field.

In the post https://www.physicsforums.com/showthread.php?t=155579 it is mentioned that a vector field could be plotted for F (x,y) by, marking the (x,y) as the tail and F(x,y) as the head portion.

If so, then consider the function, F(x,y)=(x,y)

The, if the input is (2,4) then output is (2,4)

Then, if it plotted, there will be only points everywhere right? Because, the head and the tail portion is marked at the same point.

But, when I tried the same using a online plotter (http://cose.math.bas.bg/webMathematica/MSP/Sci_Visualization/VectorField ) , I got a different result, which I have attached.
 

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  • #2
iamnotageek said:
Hi,

I have a doubt in plotting the vector field.

In the post https://www.physicsforums.com/showthread.php?t=155579 it is mentioned that a vector field could be plotted for F (x,y) by, marking the (x,y) as the tail and F(x,y) as the head portion.

If so, then consider the function, F(x,y)=(x,y)

The, if the input is (2,4) then output is (2,4)

Then, if it plotted, there will be only points everywhere right? Because, the head and the tail portion is marked at the same point.
Right.
iamnotageek said:
But, when I tried the same using a online plotter (http://cose.math.bas.bg/webMathematica/MSP/Sci_Visualization/VectorField ) , I got a different result, which I have attached.
It might be that the online graphing software doesn't handle zero vectors correctly.
 
Last edited by a moderator:
  • #3
iamnotageek said:
Hi,

I have a doubt in plotting the vector field.

In the post https://www.physicsforums.com/showthread.php?t=155579 it is mentioned that a vector field could be plotted for F (x,y) by, marking the (x,y) as the tail and F(x,y) as the head portion.
No, that's not what I said. I said:
Choose some point (x,y), Caculate the vector F(x,y)= -yi+ xi, draw that vector starting at (x,y) (with its "tail" at (x,y)).

If so, then consider the function, F(x,y)=(x,y)

The, if the input is (2,4) then output is (2,4)
You are confusing points and vectors. If you use (x, y) to mean both the point (x,y) and the vector from point (0,0) to (x,y) then you are going to be confused! Since you learned to use (x, y) to mean a point way back in "pre-Calculus", it is better to use either <x, y> or xi+ yj to denote the vector. Then F(x, y)= <x, y> or, better, F(x, y)= xi+ yj. F(2, 4)= 2i+ 4j. With its "tail" at (2, 4), its head would be at (2+2, 4+ 4)= (4, 8).

Then, if it plotted, there will be only points everywhere right? Because, the head and the tail portion is marked at the same point.

But, when I tried the same using a online plotter (http://cose.math.bas.bg/webMathematica/MSP/Sci_Visualization/VectorField ) , I got a different result, which I have attached.
 
Last edited by a moderator:

1. What is a vector field?

A vector field is a mathematical concept that assigns a vector (a quantity with magnitude and direction) to every point in a given space. In visual terms, a vector field can be represented by arrows at each point, with the length and direction of the arrows indicating the magnitude and direction of the vector at that point.

2. Why is it important to plot vector fields?

Plotting vector fields allows us to visualize the behavior and patterns of vector quantities in a given space. This can help us gain a better understanding of physical phenomena, such as the flow of fluids or the movement of charged particles in an electric field.

3. What are some common techniques for plotting vector fields?

Some common techniques for plotting vector fields include using software programs like MATLAB or Wolfram Alpha, drawing vector diagrams by hand, or using physical models or experiments to visualize the vector field.

4. How can doubt arise when plotting vector fields?

Doubt can arise when plotting vector fields due to the complexity and non-intuitive nature of vector fields. It can be challenging to accurately represent the behavior and patterns of vector fields, especially in higher dimensions or when dealing with non-linear systems.

5. What are some tips for overcoming doubt when plotting vector fields?

Some tips for overcoming doubt when plotting vector fields include using multiple visualization techniques, consulting with experts or colleagues, and thoroughly understanding the underlying mathematical concepts and principles. Additionally, practicing and experimenting with different approaches can help build confidence in plotting vector fields.

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