Let $\frac{s}{r}$ be a vector field such that: $s=-yi+xj,r=\sqrt{x^2+y^2}$
What is the domain $D$ of $\frac{s}{r}$?
My attempt:
The domain is $\{x,y\mid x^2+y^2>0\}$
Is it correct?
2026-04-22 09:46:53.1776851213
Finding domain of vector field $\frac{-yi+xj}{\sqrt{x^2+y^2}}$
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Yes, you are correct. Our only problem will be if $\sqrt{x^2+y^2} = 0$, given that $x^2+y^2 > 0$ (but this second condition always holds). But: $$\sqrt{x^2+y^2} = 0 \iff x^2+y^2 = 0 \iff x = y = 0,$$so the maximum domain is $\Bbb R^2 \setminus \{0,0\}$.