LHS KHS a) VERIFY STOKES THEOREM § ³. d² = SS (vxv).d² by showing the LHS = RHS for the vector field √ = (xz, yz, xy) such that S is the part of the Sphere x² +4² +2²=16 that lies above the X-Y plane (x, y, 2), that is, the plane z = ₂₁. b) Verify again, the theorem, for the same vector field ✓ such that S is the part of the sphere x² + y² +2²=16 that lies below the X-Y plane (x, y, z), that is below the plane z = 2

Q: Let S be the part of paraboloid z = 9 – x2 - y? with z 2 0. Verify Stokes' theorem for vector field…

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Q: 2. Verify the Stokes's Theorem for the calculation of the work done by the vector field: F = (r,y²,…

A: Stokes theorem is verified

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

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Q: 3/ MATH

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Q: Let S be the part of paraboloid z = 9 - x² - y² with z > 0. Verify Stokes' theorem for vector field…

A: Let S be the part of paraboloid z=9-x2-y2 and vector field Fx , y , z=4zi^+5xj^+2yk^. To Verify the…

Q: 31) Verify that Stokes' Theorem is true for the vector field F(x,y,z) = x² i + y² j + z² k, where S…

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Q: Calculate the curl(F) and then apply Stokes' Theorem to compute the flux of curl(F) through the…

A: The given problem is to find the curl of the given  field and also to find the flux of curl of the…

Q: Vector Field: F(x,y) = (xv, 3x, – 2y) and Surface: z = 4 - x - 3 y? Use the normal vector formula to…

A: Given surface z=4-x-3y2

Q: 3. Use Stokes' Theorem to calculate the flux of the curl of the vector field F x, x + z) across the…

A: According to the given information, it is required to calculate the flux of the curl of the vector…

Q: Let F = xyi + yzj + zæk be a vector field. Use Stokes' Theorem to evaluate f. F . dr where C is the…

A: Given that,F=xyi+yzj+zxkand the given plane is,x+y+z=1

Q: State and illustrate Stokes' Theorem using the surface of the cone z= √√²+y³ and below the plan z =…

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Q: Compute the unit normal vector field that will give the surface parametrized by r(u, v) = (e"…

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Q: Use Stokes' Theorem to evaluate curlF · dS, where

A: Let, F→=xyz , xy , x2yz. Stokes theorem states that ," Where C is the boundary of surface oriented…

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Q: (2x, 2y, 2x + 2z). Use Stokes' theorem to evaluate the integral of F around the curve consisting of…

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Q: Let F = –9zi+ (xe*z – 2xe*² ) }+ 12 k. Find f, F •dÃ, and let S be the portion of the plane 2x + 3z…

A: Given, F→=-9zi^+xexz-2xex2j^+12k^ and S be the portion of the plane 2x+3z=6 0≤y≤4

Q: F = 6x i  + 6y j + 7 k; S is "nose" of the paraboloid z = 2x 2 + 2y 2 cut by the plane z = 5;…

A: This is a problem of vector calculus.