Please help with the following three problems:

1.

Let C be the closed, piecewise smooth curve formed by traveling in a straight line between the points (0, 0, 0), (2, 1, 5), (1, 1, 3), and back to the origin in that order. Use Stokes' theorem to evaluate the integral. (11xyz) dx + (6xy) dy + xdz =Evaluate the integral / s (V X F) . dS, where S is the portion of the surface of a sphere defined by x2 + y + z = 1 and x + y + z _ 1, and where F = r x (i + j + k), r = 5xi + 5yj + 5zk. (Assume that the sphere is outward oriented so that the normal of S has a positive k component.) (Express numbers in exact form. Use symbolic notation and fractions where needed.) (V X F) . dS = SLet F = (12xe)) i - (2x cos(z)) j - (12ze)) k. Find a G such that F = V X G. Instruction: Follow the outline of the proof of Theorem 8 from Exercise 18.101 in the Exercises to Section 18.3 in your Ebook. Particularly, start by setting G3 = 0. (Write your solution using the form (*,*,*). Use symbolic notation and fractions where needed.) G =