Let \(\mathbf{F}=\left\langle-z^{2}, 2 z x, 4 y-x^{2}ightangle\), and let \(C\) be a simple closed curve in the plane \(x+y+z=4\) that encloses a region of area 16 (Figure 20). Calculate \(\oint_{C} \mathbf{F} \cdot d \mathbf{r}\), where \(C\) is oriented in the counterclockwise direction (when viewed from above the plane).

4 Z x+y+z=4