[S S Use Stokes' Theorem to evaluate curl F. dS where F = (x + y)i + (y − x + 3) j + e^²+y−² k and S is defined by x² + y² + z² = 1, z ≥ 0 and n points outward.

Q: 2. Let vector field F=(xz,-y,z) and surface, S is a cylinder x+y = 4 for 3<z<0 with %3D outward…

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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: 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: Verify the validity of the Stokes's theorem for the vector A = e-bz sin ø a, + pe-bz , over the open…

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Q: Find div(curl F) = V. (V x F). F(x, y, z)= xyzi + yj + zk

A: If vector field then from the question

Q: Let F-yi + xyj+-xyzk and let Σ be the part of the cone z =sqroot(x^2 +y^2(Figure 3) for 0 < x²+ y²…

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Q: Use Stokes' Theorem to find the circulation of F = 4yi + 4zj+ 3xk around the triangle obtained by…

A: We have to find ∫CF→·dr→ using Stokes'sTheorem

Q: Use Stokes' Theorem to find the circulation of F = 4yi +7zj +3ck around the triangle C' obtained by…

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Q: Is there a vector field G on R³ such that curl G = (x sin y, cos y, z - xy)? Explain

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Q: If F(x, y, z)= xz i  + xyz j - y 2 k find curl F

A: given: F(x,y,z)=xzi+xyzj-y2k we have to find the curl F. as we know that if we have F→=Fxi+Fyj+Fzk…

Q: Find the work done by the force field F(x, y) = 2xy³i+ 4x²y² in moving a particle counterclockwise…

A: The work done of a force F→ along a curve r→ is defined by ∫CF→⋅dr→.Since curve is closed in…

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: Use Stokes' Theorem to find the circulation of F = 5yi + 3zj + 6xk around a circle C of radius 7…

A: Stokes' Theorem: The formula for Stokes' Theorem is given by:         ∫CF→·dr=∬RCurl F→·n→ dA where…

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

Q: Let I be the curve parametrised by 2t 2(4) = ( sin(zt), 41' Vt +1 for 0<t<1 t2 +1' and let F be the…

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Q: to be careful to choose a parametrization r(u, v) that determines the correct counterclock- wise…

A: As per the question we are given a statement regarding the Stoke's Theorem and we have to say if it…

Q: 26. Verify Stokes' Theorem for the vector field F = 2xyi + xj + (y+z)k and surface z = 4x² - y², z ≥…

A: The given problem is to verify the stokes theorem for the given vector field over the given surface…

Q: Use Stokes' Theorem to find the circulation of F = 2yi + 3zj + 7xk around the triangle obtained by…

A: Here we have to solve the given problem using stokes' theorem.

Q: Evaluate the circulation of G = ayi+zj+ 7yk around a square of side 9, centered at the origin, lying…

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Q: What is the largest possible magnitude of Curl(F) where F(x, y, z) = (4, a/9 – y?, 6z)? у, х

A: Given that F→x,y,z=4,x9-y2,6z

Q: Let f = (r +2ryz)i+( + 2xy)j+ (+ 2xyz)k. Find j at (1.0, 1). (a) divergence of

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Q: H.W: Select the divergence of F(x, y) i+ (2x – 3y)j. %3D 1 (b) -* +2, y2 1 (c) (a) 3, (d) -2. - - -

A: Multiple:   Divergence of a vector field find by taking the scalar product of the vector operator  ∇…