Evaluate $\int _ { C } \mathbf { F } d \mathbf { r }$

Evaluate $\int _ { C } \mathbf { F } d \mathbf { r }$ where $\mathbf { F } ( x , y , z ) = \left\langle \frac { z } { x - y } , \frac { z } { y - x } , \ln ( x - y ) \right\rangle$ and C is the circle $( x + 2 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1$ in the clockwise direction.

A) $6$
B) $- 2$
C) $- 4$
D) $1$
E) $- 6$
F) $2$
G) $4$
H) $0$

Correct Answer:

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