Let o be the surface 3r+ 10y+9z = 4 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 (5z - 8y) i + (8y – 102) j + (10z – 5z) k using line integrals, and using Stoke's 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

Calculus: Early Transcendentals
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Let o be the surface 3r + 10y + 9z = 4 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 (5r - 8y) i+ (8y – 10z) j + (10z – 5x) k using line
integrals, and using Stoke's 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 <t< 1, 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
F. dr=
F dr=
F dr-
C3
F dr =
STOKE'S THEOREM
a may be parameterized by r(r, y) = (r,y, f(r,y)) =
curl F.
Transcribed Image Text:Let o be the surface 3r + 10y + 9z = 4 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 (5r - 8y) i+ (8y – 10z) j + (10z – 5x) k using line integrals, and using Stoke's 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 <t< 1, 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 F. dr= F dr= F dr- C3 F dr = STOKE'S THEOREM a may be parameterized by r(r, y) = (r,y, f(r,y)) = curl F.
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
F dr=
F dr =
%3D
F dr =
F dr=
%3D
STOKE'S THEOREM
o may be parameterized by r(r, y) = (r, y, f(r,y)) =
curlF=
(curl F) - nds =
dy dr
Transcribed Image Text: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 F dr= F dr = %3D F dr = F dr= %3D STOKE'S THEOREM o may be parameterized by r(r, y) = (r, y, f(r,y)) = curlF= (curl F) - nds = dy dr
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