i have a question in stokes theorem, and i am having trouble finding the

normal vector.

we have a curve $\displaystyle C = {(x,y,z)| x^2+z^2=16, y=8}$

and our goal is to calculate the work done by the field

$\displaystyle F = [6z^3]i+[5y^2]j-[6x^3]k$ along the curve.

so i use stokes theorem, and pick a surface S enclosed by C:

$\displaystyle S = {(x,y,z)| x^2+z^2<=16, y=8}$

and the normal vector N, will be in the (-j) direction.

eventually what i get is using stokes theorem:

$\displaystyle \int\int_S [(18x^2+18z^2)]nds$

How do i find the length and direction of the normal vector n?

thanks in advance