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

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

irishboy123 · Answer

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