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Lancelot59

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**Proving Magnitude Of Vector Valued Function Is Constant**

I have a rather neat problem. I need to prove that the magnitude of this function:

[tex]F_{2}(x,y)=\frac{<-x,y>}{x^{2}+y^{2}}[/tex]

is constant along circles centred about the origin. Now while proving that the magnitude is inversely proportional I had to get the magnitude, and it wound up being:

[tex]\sqrt{\frac{1}{(x^{2}+y^{2})}}[/tex]

Which looks like the basic equation for a circle to me. That particular function will give elliptical level curves. I'm not sure how to go about this. Can I just say that because it's the inverse of a the form of an ellipse that if the level curve x^2+y^2 is equal to a constant c^2 then the magnitude will also be a constant because it has the same form?

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