An application of vector fields is when the vectors represent force. Let F(x,y,z) be a force field. We say that the work done by the force field F(x,y,z) over the curve C is given by the equation
Work = ∫CF(r)⋅dr∫CF(r)⋅dr∫CF(r)⋅dr∫CF(r)⋅dr
Where r(t) is some parameterization of C. Let F(x,y,z) be given by the function F(x,y,z)=(x−y^2)i+(y−z^2)j +(z−x^2)k. Suppose that a particle moves through the force field F(x,y,z) along the line segment running from the point (1, 1, 1) to the point (-1, 2, -1). Using the parameterization r(t)=(1−t)(1,1,1)+t(−1,2,−1), at what time t will the force field F(x,y,z) have done 2.5 units of work on the particle? Round your answer to two decimal places.
(Hint: you will want to use theFindRoot command inMathematicain order to solve this problem)