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## Homework Statement

## Homework Equations

W= ∫F.dr

## 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, 3t

^{2}, 2t)

Which gives ∫F.dr = (-t, 3t

^{2}, 2t )(-1,-1,-1)dt

= ∫ (t -3t

^{2}- 2t) dt

= [t

^{2}/2 - t

^{3}- t

^{2}] , 0<t<1

= -3/2 units of work

So am I right? Or mostly right? Or mostly wrong? Or totally wrong?

Thanks a lot!