Calculate the work done by the field \(\mathbf{F}\) when the object moves along the given path from the initial point to the final point.

\(\mathbf{F}(x, y, z)=\langle x y, y z, x zangle, \mathbf{r}=\left\langle t, t^{2}, t^{3}ightangle\) for \(0 \leq t \leq 1\)