Let be the surface 10x+5y+6z=4 in the first octant, oriented upwards. Let C be the oriented boundary of . Compute the work done in moving a unit mass particle around the boundary of through the vector field F=(3x10y)i+(10y2z)j+(2z3x)k using line integrals, and using Stokes' Theorem. Assume mass is measured in kg, length in meters, and force in Newtons (1nt=1kgm). LINE INTEGRALS Parameterize the boundary of positively using the standard form, tv+P with 0t1, starting with the segment in the xy plane. C1 (the edge in the xy plane) is parameterized by C2 (the edge following C1 ) is parameterized by C3 (the last edge) is parameterized by C1Fdr=C2Fdr=C3Fdr=CFdr= STOKES' THEOREM may be parameterized by r(x,y)=(x,y,f(x,y))= curlF= xryr= (curlF)ndS= dydx Let be the surface 10x+5y+6z=4 in the first octant, oriented upwards. Let C be the oriented boundary of . Compute the work done in moving a unit mass particle around the boundary of through the vector field F=(3x10y)i+(10y2z)j+(2z3x)k using line integrals, and using Stokes' Theorem. Assume mass is measured in kg, length in meters, and force in Newtons (1nt=1kgm). LINE INTEGRALS Parameterize the boundary of positively using the standard form, tv+P with 0t1, starting with the segment in the xy plane. C1 (the edge in the xy plane) is parameterized by C2 (the edge following C1 ) is parameterized by C3 (the last edge) is parameterized by C1Fdr=C2Fdr=C3Fdr=CFdr= STOKES' THEOREM may be parameterized by r(x,y)=(x,y,f(x,y))= curlF= xryr= (curlF)ndS= dydx