F is the three-dimensional vector field defined by F(x,y,z) = ( z, x, y ). In other terms, P(x,y,z) = z, Q(x,y,z) = x, R( x,y,z) = y. Also, the domain T is the equilateral triangle in space with...

F  is the three-dimensional vector field defined by F(x,y,z) = ( z, x, y ).  In other terms,

P(x,y,z) = z, Q(x,y,z) = x, R( x,y,z) = y.

Also, the domain  T  is the equilateral triangle in space with vertices (corners) at

( 2, 0, 0 ), ( 0, 2,0 ), ( 0, 0, 2 ), and normal vector n = ( a, b, c )  with  a > 0 AND b > 0 AND c > 0.

The boundary, or perimeter,  C  of the triangle  T   consists of three straight segments, oriented counterclockwise from (2,0,0) to (0,2,0), then from (0,2,0) to (0,0,2), and back from (0,0,2) to (2,0,0).

Question:  Calculate the circulation (line integral) of  F  around the boundary   C   of the triangle  T.