Some Math people help me with this before I lose my mind

So we got ya boy Stokes Theorem:

∬R(∇×F)∙n^dS=∮∂RF∙dp

∮C(x−y)dx+(x−2y+z)dy+(3x+z)dz

C is parameterized by p(t)=⟨cos(t),sin(t),3⟩, 0≤t<2π

So I get ∇×F(x,y,z) = <-1, -3, 2> ezpz

but then for n they get <0, 0, 1> and they don't explain how and I can't figure it out. Someone pls help me I don't get it.

Edit:

Here's a screenshot if it makes it easier to read

https://i.imgur.com/kWcjxyo.png