Doubt in plotting Vector Fields

AI Thread Summary
The discussion revolves around the confusion in plotting vector fields, particularly the function F(x,y) = (x,y). It is clarified that while (x,y) represents a point, F(x,y) should be interpreted as a vector, leading to a different plotting outcome. The user initially believes that plotting this function results in only points, as the tail and head of the vector coincide. However, the response emphasizes the importance of distinguishing between points and vectors, suggesting that the vector should be represented as xi + yj for clarity. The online plotter may yield different results due to its handling of vector representations.
iamnotageek
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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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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.
 
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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.
 
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