Let o be the surface 10x +7y +8z = 2 in the first octant, oriented upwards....

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Let o be the surface 10x +7y +8z = 2 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 = (9x - y)i + (y - 8z)j +(8z - 9x)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 a positively using the standard form, tv+P with 0 ≤ t≤ 1, starting with the segment in the xy plane. C₁ (the edge in the xy plane) is parameterized by <1/5-1/5t,2/7t> C2 (the edge following C₁) is parameterized by <0,2/7-2/7t,1/4t> C3 (the last edge) is parameterized by <1/5t,0,1/4-1/4t> Je Sci F.dr= -421/2450 F.dr = 0 √F-dr=0 F dr= F.dr. = 151/8 (2/7*(1/5)-(10 (1/5)^2/1 JC₂ la F.dr = 0 [F F.dr = Ər əx STOKES' THEOREM o may be parameterized by r(x, y) = (x, y, f(x, y)) = <x,y, (2-10x-7y)/8> 151/8*(2/7*(1/5)-(10*(1/5)^2/1 curl F = <8,9,1> ду = <5/4,7/8,1> (curl F). ndS = = 1/5 0 (2-10x)/7 0 151/8 151/8*(2/7*(1/5)-(10*(1/5)^2/1 Let o be the surface 10x +7y +8z = 2 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 = (9x - y)i + (y - 8z)j +(8z - 9x)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 a positively using the standard form, tv+P with 0 ≤ t≤ 1, starting with the segment in the xy plane. C₁ (the edge in the xy plane) is parameterized by <1/5-1/5t,2/7t> C2 (the edge following C₁) is parameterized by <0,2/7-2/7t,1/4t> C3 (the last edge) is parameterized by <1/5t,0,1/4-1/4t> Je Sci F.dr= -421/2450 F.dr = 0 √F-dr=0 F dr= F.dr. = 151/8 (2/7*(1/5)-(10 (1/5)^2/1 JC₂ la F.dr = 0 [F F.dr = Ər əx STOKES' THEOREM o may be parameterized by r(x, y) = (x, y, f(x, y)) = <x,y, (2-10x-7y)/8> 151/8*(2/7*(1/5)-(10*(1/5)^2/1 curl F = <8,9,1> ду = <5/4,7/8,1> (curl F). ndS = = 1/5 0 (2-10x)/7 0 151/8 151/8*(2/7*(1/5)-(10*(1/5)^2/1