Verify the Stokes's Theorem for the calculation of the work done by the vector field: F = (r, y², xz) along the contour of the surface defined as: S == {(x, y, z) E R* : a² + y² + z² = 1, x > 0; y 2 0; z 2 0}

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

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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,…

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Q: 3/ MATH

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Q: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u ER…

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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…

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Q: Verify Stokes theorem for the vector field F = 2(-+x)i- z? yj-zyk over the upper half x² +y? +z?…

A: To verify Stokes' Theorem for the vector field               F→=2-y2+xi→-z2yj→-zy2k→ over the upper…

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

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Q: 4. Confirm Stokes' theorem for the vector field F(x.y.z)= (0, yz, xz) for the plane surface z =1-y…

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Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

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: Calculate the surface integral ( i.e. f(y x F) · dS )of the curl of the vector field: F(r, 6, 2) =…

A: The given vector field is  F→(r, ϕ, z)=1π8ϕ^+2z^

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

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Q: Evaluate the line integral by stokes theorem where F(vector)=[ 0, xyz ,0] , C is the boundary of a…

A: Calculate curl:  curlF=ijk∂∂x∂∂y∂∂z0xyz0         =i-xy+kyz

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

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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.

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