How to Apply Stoke's Theorem When Unable to Express Z in Terms of X and Y?

[fonseh]

Homework Statement

i can't find the normal vector here . In my book , outwards vector is . (Refer to photo 1 )
The question is in photo 2 , i am aksed to use stoke's theorem to evalutae line integral of vector filed
But , now the problem is i can't express z in terms of y and x . Can anyone help ?

Homework Equations

The Attempt at a Solution

For now , i have Δx F = (-z+ 1) j only

 

[Charles Link]

Homework Statement

i can't find the normal vector here . In my book , outwards vector is . (Refer to photo 1 )
The question is in photo 2 , i am aksed to use stoke's theorem to evalutae line integral of vector filed
But , now the problem is i can't express z in terms of y and x . Can anyone help ?

Homework Equations

The Attempt at a Solution

For now , i have Δx F = (-z+ 1) j only

For your first case, I don't see a boundary line to the surface. For the second case, the surface is a cylinder, and I think they might be asking you to compute $\int \vec{F} \cdot \, dS$. If that is the case, you could also use Gauss law and compute $\int \nabla \cdot \vec{F} \, d^3x$, but certainly not Stokes theorem. (the Gauss's law version would also include in its result the integration over the endfaces of the cylinder). $\\$ Additional item: For vector curl use " \nabla \times " in Latex. To get Latex, put " ## " on both sides of your statement or expression. (The vector gradient is " \nabla" in Latex. The divergence is " \nabla \cdot ".)

 

[LCKurtz]

Homework Statement

i can't find the normal vector here . In my book , outwards vector is . (Refer to photo 1 )
The question is in photo 2 , i am aksed to use stoke's theorem to evalutae line integral of vector filed
But , now the problem is i can't express z in terms of y and x . Can anyone help ?

Homework Equations

The Attempt at a Solution

For now , i have Δx F = (-z+ 1) j only

What is preventing you from typing in a complete statement of the problem? There is no question in the photo telling us what line integral (if it really is a line integral) you want.