Let F be a constant unit force that is parallel to the vector (-1,0,1) in xyz-space. What is the work done by F on a particle that moves along the path given by (t,t^2,t^3) between time t=0 and time t=1.

a) -1/4

b) -1/(4root(2))

c) 0

d) root(2)

e) 3root(2)

I did it wrong but my method was to take the projection of (t,t^2,t^3) on (-1,0,1)

Then integrating from 0 to 1. My answer was -1/4 (which is wrong its supposed to be 0) how did you guys do it?