Chapter 6.8, Problem 7P

For the force field $F=(y+z)i-(x+z)j+(x+y)k,$ find the work done in moving a particle around each of the following closed curves:

(a) the circle $x^2+y^2=1$ in the $(x,y)$ plane, taken counterclockwise;

(b) the circle $x^2+z^2=1$ in the $(z,x)$ plane, taken counterclockwise;

(c) the curve starting from the origin and going successively along the $x$ axis to $(1,0,0),$ parallel to the $z$ axis to $(1,0,1),$ parallel to the $(y,z)$ plane to $(1,1,1)$ and back to the origin along $x=y=z$;

(d) from the origin to $(0,0,2\pi )$ on the curve $x=1-\cos t,y=\sin t,z=t,$ and back to the origin along the $z$ axis.