The Attempt at a Solution
I'm fairly sure I've done the right thing, however my lecturer hasn't uploaded any solutions to any of these problems (which is ridiculous - how am I supposed to learn if I don't know when I'm right or wrong?!) So I'm putting it over to physics forums for some general opinion on my answer.
The path between (1,4,2) and (0,5,1) is a simple move of (-1,-1,-1),
This parameterises to a move of (-t,-t,-t) for 0<t<1
and means x= -t, y= -t, z= -t
so dr = (-t,-t,-t) = (-1,-1,-1)dt
and F = (x, 3xy, -(x+z)) = (-t, 3t2, 2t)
Which gives ∫F.dr = (-t, 3t2, 2t )(-1,-1,-1)dt
= ∫ (t -3t2 - 2t) dt
= [t2/2 - t3 - t2] , 0<t<1
= -3/2 units of work
So am I right? Or mostly right? Or mostly wrong? Or totally wrong?
Thanks a lot!