Final answer:
To find the work done by the force field, we can use Stokes' Theorem and calculate the circulation of the field around the closed path formed by the line segments.
Step-by-step explanation:
The work done by the force field can be calculated using Stokes' Theorem. Stokes' Theorem states that the work done by a force field along a closed path is equal to the circulation of the field around the path. In this case, the closed path is formed by the line segments from the origin to (2, 0, 0), (2, 3, 1), (0, 3, 1), and back to the origin.
To calculate the circulation of the force field, we need to find the line integral of the force field over the closed path. The line integral of a vector field F along a curve C is given by ∫C F · dr, where dr is the differential displacement vector along the curve. In this case, the curve C is the closed path formed by the line segments.
To evaluate the line integral, we can use the parametric equations of each line segment to express dr in terms of a single parameter t. Then we can substitute these equations into the line integral expression and integrate over the parameter t.