Question

Let
F = (z − y) i  + (x − z) j  + (y − x) k 
. Let C be the rectangle of width 2 and length 3 centered at (7, 7, 7) on the plane x + y + z = 21, oriented clockwise when viewed from the origin.

Use Stokes' Theorem to find
F * dr

Answer 1

the curl is numerical so to me looks like no integration needed, just dot the curl with the unit normal, then times 6.