Take a 3D surface R with boundary curve C. If you are given a vector field Field[x, y, z] with the extra property that curlField[x, y, z], with its tail at {x, y, z}, is tangent to the surface R at all points {x, y, z} on the surface R, then how does Stokes's formula tell you that the net flow of Field[x, y, z] along C is 0?

firstly,3D gradient field has zero curl

Stoke's Theorem says that the flow along is the double integral of CurlField[x,y,z] is unit normal.

Step-by-step explanation:

3D gradient field has zero curl.

Stoke's Theorem says that the flow along is the double integral of CurlField[x,y,z] is unit normal. If CurlField[x,y,z] is tangent to the surface everywhere, it is perpendicular to the unit normal everywhere. So the flow is the integral of 0, and hence the net flow is 0.

this was already solved by me with a different person. if you look it up in the search bar at the top of the page, you will get the answer.

step-by-step explanation:

it is b)

hope this : )

step-by-step explanation: