Evaluate integral where $C$ is the path of straight line segments in 3D

Question

I am confused how to solve this because it is integral over 3D line segments:

Let $\vec{F}(x,y,z) = \left\langle\frac{z^2}{x},\frac{z^2}{y},2z\ln(xy)\right\rangle$ Evaluate $\int_C \vec{F}\, \cdot d\vec{s}$ where $C$ is the path of straight line segments from $P = (1, 2, 1)$ to $Q = (4, 1, 7)$ to $R = (5, 11, 7)$, and then back to $P$.

Answer 1

Hint:

The curl of a vector field $\vec{F}$ is nul-vector, i.e. $\operatorname{rot}\vec{F}=\vec{0}.$