STOKES' THEOREM o may be parameterized by r(2, y) = (z, y, f(x, y)) = curl F (curl F) - nds %3D dydz 54/(sqrt140)

Extracted text: STOKES' THEOREM o may be parameterized by r(2, y) = (z, y, f(x, y)) = curl F (curl F) - nds %3D dydz 54/(sqrt140)


Extracted text: Let o be the surface 10r + 2y + 6z = 8 in the first octant, oriented upwards. Let C be the oriented boundary of a. Compute the work done in moving a unit mass particle around the boundary of o through the vector field F = (4x – 3y)i + (3y – 2)j + (z– 4x)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 <>< 1,="" starting="" with="" the="" segment="" in="" the="" xy="" plane.="" c="" (the="" edge="" in="" the="" xy="" plane)="" is="" parameterized="" by=""><4 5-4/5t,41,0=""> C2 (the edge folowing C1) is parameterized by <0,4-41,4 3t=""> C3 (the last edge) is parameterized by <4 5t,0,4/3-4/3t=""> F dr= 688/25 C1 dr = -136/9 F-dr = dr= STOKES' THEOREM