Find the work done by the force field f on a particle moving along the given path. f(x, y, z) = yzi + xzj + xyk c. line from (0, 0, 0) to (9, 7, 4)

Computing the line integral directly would be easy enough, but in general it's worth checking to see if the vector field is conservative; that is, whether there exists a scalar function whose gradient corresponds exactly to the given vector field , or . Equivalently, we're looking for such that





We find that





and so there is indeed such a function , with .
Thus by the fundamental theorem of calculus, the line integral is path-independent, and



where is any path starting at and ending at . Here,