# Stokes equation help

## Homework Statement

let F be vector field:
$$$\vec F = \cos (xyz)\hat j + (\cos (xyz) - 2x)\hat k$$$
let L be the the curve that intersects between the cylinder $$$(x - 1)^2 + (y - 2)^2 = 4$$$ and the plane y+z=3/2
calculate:
$$$\left| {\int {\vec Fd\vec r} } \right|$$$

## Homework Equations

in order to solve this i thought of using the stokes theorem because the normal to the plane is $$$\frac{1}{{\sqrt 2 }}(0,1,1)$$$
thus giving me
$$\oint{Fdr}=\int\int{curl(F)*n*ds}=\int\int{2/sqrt{2}*\sin(xyz)}$$

i tried to parametries x y and z x= rcos(t)+1 y=rsin(t)+2 z=1/2-rsin(t)

but it wont work

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Would x = 1 + 2 cos(t), y = 2 + 2 sin(t) and z = -1/2 - 2 sin(t) do the trick?

i wonder if it is allowed given we have to do a multiple integral needing 2 variables

Why wouldn't you just use Green's?

using green or stokes is the same thing green is just a private solution of stokes and if you use it you are still stuck with that sin(xyz)