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Sketch the vector field by drawing representative non intersecting vectors with initial points $(1, 1), (-1, 1), (-1,-1), (1,-1), (2, 2), (-2, 2),(-2,-2), (2,-2)$. The vectors need not be drawn to scale, but they should be in reasonably correct proportion relative to each other.

$$F(x, y) = \frac{xi + yj}{(x^2 + y^2)^\frac{1}{2}}$$

With the help of your diagram describe in words how the field is oriented and magnitude of the vector near the origin.

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Welcome to math.SE! Most questions here pertain to mathematical equations and proofs or discussions, thus a graphical question may not be the best to pose. However, if you ask how you might go about answering such a question, rather than ask for a drawing, you will likely get better results. Could you give more detail regarding the field the points are in, and if possible some motivations and thoughts on the problem? – adam W Feb 7 '13 at 3:01
Please check that my edits are correct, especially if the numerator in the fraction pertains to both elements, or to only the one element as you had originally. – adam W Feb 7 '13 at 3:14
@ adam W .Its correct. sorry for adding the function later. could the plot be done manualy – Avinesh Feb 7 '13 at 3:18
@Avinesh: turn $yi$ to $yj$ above in $F$. – Babak S. Feb 7 '13 at 5:15
The phraseology "non-intersecting vectors" seems rather odd. Did you (or your instructor) really mean "divergent"? – DWin Jul 14 at 2:57

I made it via Maple 16:

enter image description here

Here is its code:

[> with(Student[VectorCalculus]):

[> VectorField((x, y*(1/sqrt(x^2+y^2))), output = plot, view = [-4 .. 4, -4 .. 4], scaling = constrained, color = "NavyBlue", fieldoptions = [fieldstrength = fixed, arrows = SLIM, grid = [10, 10]]);

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Nice, +1. I think I missed that he actually gave a function there... – adam W Feb 7 '13 at 3:07
@Babak Sorouh Thanks alot. Is there any method to draw manualy – Avinesh Feb 7 '13 at 3:14
@Avinesh: Yes , it is easy just be giving the function some points like $(x,y)$. So, after doing that, you would get some, for example, 10 vectors like $xi+y/\sqrt{x^2+y^2}j$. It can be done by hand. Sorry if I misuse Maple. Maybe you wanted it by hand. – Babak S. Feb 7 '13 at 3:19
@Babak Sorouh. thanks that information is quite helpful. i checke an example at – Avinesh Feb 7 '13 at 3:25
@Avinesh: $F$ is clearly not defined at the origin. – Babak S. Feb 7 '13 at 5:16

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