Let o be the surface 4x + 6y + 8z = 5 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 = (7x - 6y)i + (6y − 8z)j + (8z – 7x)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 ≤ 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 Sai F. dr = Ja F.dr = Je₂ F.dr = fo F.dr = STOKES' THEOREM o may be parameterized by r(x, y) = (x, y, f(x, y)) = | curl F = ox ff (c (curl F) · ndS= TIO dydz

Q: F= (y, 2x, -z) and C is the circle x² +y² = 9

A:

Q: The integer n = 12700140x3243243 is missing the digit x. a) If n congruent to  3 (mod 9), then what…

A: According to the given information, Consider the given integer n:

Q: Let S be the part of the plane 3r + ly +z = 3 which lies in the first octant, oriented upward. Use…

A: given plane 3x+y+z=3 which lies in the first octant oriented upward.  use stokes theorem to find the…

Q: Calculate the flux of the vector field V = 5i through a square of sides 4 m in the y-z plane (0 s ys…

A: Given V = 5i Area oriented towards positive x direction

Q: Use Stokes theorem to find the work performed by the force field F= (x. xy',xy') on a particle that…

A: Given that: F→=x3, xy3, xy2F→=x3i^+ xy3j^+ xy2k^ And: φ=z-y∇φ=i∂∂x+j∂∂y+k∂∂zz-y∇φ=-j+k The unit…

Q: Calculate the vector field flow g⟶ (x,y,z) = (y) î - (x) j + (x + y) k, counterclockwise, along the…

A:

Q: Verify Stokes' Theorem for the given vector field and surface, oriented with an upward - pointing…

A:

Q: 3) Given the vector field F = circulation around the triangle formed by the intersection of the…

A:

Q: Verify Stokes' Theorem for the given vector field and surface, oriented with an upward-pointing…

A: For the vector field  and the surface  where  oriented with an upward pointing normal we have to…

Q: It is estimated that 60% of emails are spam emails. Some software has been applied to filter these…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the flux of the vector field  V(x, y, z) = 3xy2i + 3x2yj + z3k out of the unit sphere. Use the…

A: Sol:- The surface integral of a vector field V over a closed surface S is given by: ∬SV.dS=∫∫∫V.n dV…

Q: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 5 for fluid flowing…

A:

Q: A particle moves along line segments from the origin to the points (3, 0, 0), (3, 5, 1), (0, 5, 1),…

A:

Q: Find the flow rate of F = across the portion of the surface z = over the unit square [0, 1] × [0, 1]…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Let S be the part of the plane 4x + 3y + z = 4 which lies in the first octant, oriented upward. Use…

A:

Q: Use Stokes' Theorem to find the work done by the force field F= on a particle that traverses counter…

A: Given data: The force field is F→=z3,12x,y The equation of circle is C:x2+y2=9 in the plane z=5.

Q: Use Stokes' theorem to calculate the integral for the surface S and boundary aS, and the given…

A: S={(x,y,z): x2+y2+z2=64, z≥0} This is an equation of a sphere We take an element in the (x,y) plane…

Q: (b) Verify Stokes Theorem for the vector field F = zî + xĵ + xk and the hemi- spherical shell S…

A: (b)  According to stokes theorem we have,

Q: (c) Calculate the flux of the vector field F = xi+yj + zk outwards the curved surface of the…

A: