Let o be the surface which is the part of the graph of 10x + 7y + 5z = 10 in the first octant, oriented upwards. Let C be the oriented boundary of o. Compute the work done in moving a unit mass particle around the boundary of o through the vector field F = (2x - y)i + (y - 9z)j + (9z - 2x) k using line integrals, and using Stokes' Theorem. Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m). LINE INTEGRALS Parameterize the boundary of o positively using the standard form, tv+P with 0 C2 (the edge following C1) is parameterized by C3 (the last edge) is parameterized by F . dr = F . dr = F . dr = F . dr =[ STOKES' THEOREM " may be parameterized by r(x, y) = (x, y, f(x, y)) = or or (curl F) . ndS = 0 0