\text { Consider the force field } \overrightarrow{\mathbf{F}}=(x+2 y z) \hat{\mathbf{i}}+(y+2 x z) \hat{\mathbf{j}}+(z+2 x y) \hat{\mathbf{k}} \text {. } a) Evaluate the curl of F, i.e. VxF. Is the field conservative? If so, find a potential function for it. b) By using the potential function in a), find the work done in moving a particle from the origin to (1,2,3). c) By formulating a direct line integral, show that the same work done in b) can be obtained by using a straight line path. d) Without showing any calculations, analyse the work done in moving a particle from the origin to (1,2,3) and back to the origin.