Let

C$1$

and

C$2$

be two smooth parameterized curves that start at

P$0$

and end at

Q$0$ P$0,$

but do not otherwise intersect. If the line integral of the vector field

F$($x$,$ y$,$ z$)$

along

C$1$

is equal to $45\mathrm{.}4$ and the line integral of

F$($x$,$ y$,$ z$)$

along

C$2$

is

$16\mathrm{.}6,$

what is the line integral around the closed loop formed by first following

C$1$

from

P$0$

to

Q$0,$

followed by the curve from

Q$0$

to

P$0$

along

C$2,$

but moving in the opposite direction?