I was able to get this question correct but now I can't.

LetFbe a constant unit force that is parallel to the vector $\displaystyle <-1,0,1>$ in xyz-space. What is the work done byFon a particle that moves along the path given by $\displaystyle (t,t^2,t^3)$ between time $\displaystyle t=0$ and time $\displaystyle t=1$?

$\displaystyle W=cos(\theta)\parallel F\parallel \parallel PQ\parallel $

$\displaystyle cos(\theta)=\frac{<,u,v>}{\parallel u\parallel \parallel v\parallel}$

simplifies down to:

$\displaystyle W=<u,v>=<F,PQ>$

For PQ, I have (but something is wrong since the answer is 0) $\displaystyle 0\leq x\leq 1, t\mathbf{i}+t^2\mathbf{j}+xt^3\mathbf{k}$

$\displaystyle W=-t+t^3\neq 0$