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bitrex
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Homework Statement
I'm supposed to sketch the vector field and verify that all the vectors of the following equation have the same length.
Homework Equations
[tex]G(x,y) = \frac{-iy + jx}{\sqrt{x^2+y^2}}[/tex]
The Attempt at a Solution
If I start plugging in numbers, for example the point (1,1) into [tex]\frac{-iy}{\sqrt{x^2+y^2}}[/tex] and into [tex]\frac{jy}{\sqrt{x^2+y^2}}[/tex] I move minus 1 unit along the x axis, and up one unit along the Y axis. So that vector has a length of 1 unit. But if I put in (2,2) to the same equation I move [tex]\frac{-2}{\sqrt{8}}[/tex] in the negative X direction and the same in the positive Y direction. I don't see ho..Oh. Now that I'm typing it out in LaTeX I see it. If I take the magnitude of the new i,j vector I get from evaluating the equation, I'm going to get 1 aren't I? And no matter what values I plug into the original equation, the magnitude of the resulting vector is always going to work out to 1. Does that sound correct?
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