c) Use Stokes' theorem to evaluate F. dr where F = z' i+yJ + xk and C is the triangle with vertices (2,0,0), (0, 2, 0) and (0,0, 2) with anticlockwise direction when viewed from above.

Q: Find the coordinates of the centroid of the curve given belov x = cos t+tsin t, y =t cos t- sin t,…

A: Given data: The x-coordinate of the curve is x=cos t+tsin t. The y-coordinate of the curve is y=tcos…

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Q: 11. Use Stokes' Theorem to evaluate OF dr where F=(xz,e",y+z) on the curve that is the intersection…

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Q: Use stokes theorem to evaluate f.dr where f = (4z+y, 3x, 7y) and C is the curve of intersection of…

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Q: Find the work done by the force F(x , y , z)=(xyz ,−cos (yz), xz)moving a particle along a line…

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Q: 4. Use Stokes’ theorem to evaluate fa F. dr, where F(x,y, z) = (xy,yz, zx), and C is the triangle…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: D

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Q: (5) Use Stokes' Theorem to find the line integral |(* + 2y°)i + (y + z°) +(= + 2r*)k) • dř where C…

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Q: Use Stokes' theorem to evaluate Ĝ - dĩ, vhere Ĝ(1, Y, 2) = (2r, y,0) and D is any closed curve.

A:

Q: Find the coordinates of the centroid of the curvex = et cos t, y = et sin t, 0 ≤ t ≤ p.

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Q: and v ∈ [1, 3], which describes the surface S represented in the following graph: image1 A normal…

A: Consider the parametrization r (u, v) = (v, 2 cos u, 4 sin u), with u ∈ [ 0 , π/2]and v ∈ [1, 3],…

Q: 2) Using Stokes theorem, evaluate pvdr where v= 2y'i– 2x° j+÷k_and the C is the curve of C…

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Q: The curve y = sin(πz), with 0 ≤ z ≤ 2, on the yz-plane is revolved once about the z-axis. Find a…

A: Given that y=sin πz and 0≤z≤2 The objective is to find the vector equation. The image formed is like…

Q: Use Green's theorem to evaluate $(xy + 3x²)dx + (3y – 2x)dy, along C, where Cis the triangle with…

A: Given Integral ∮(xy+3x2)dx +(3y-2x)dy along c where c is the triangle with vertices (0, 0), (0, 3)…

Q: Use Stokes' Theorem to compute 1 z? dx + (ry) dy + 2020 dz, where C is the triangle with vertices at…

A: Given I=∮C12x2+xydy+2020dz where C is the triangle with vertices at 1,0,0 , 0,2,0 , 0,0,2 traversed…

Q: Use Stokes' theorem to evaluate frotF. ds. F(x, y, z) = xyi + e²j + xy²k; S consists of the four…

A: To find- Use Stokes' theorem to evaluate ∫SrotF·dS, Fx, y, z = xyi + e2j + xy2k; S consists of the…

Q: The plane z =0 separates region 1 (z 0), which is a dielectric material with ɛ, = 4, from region 2…

A: The complete solutions are given below

Q: z = In(x²y*) + / x² + y²

A:

Q: 6. Use Stokes theorem to evaluate $. F•dr, where F = (-3y² , 4z, 6x) and C is the triangle in the…

A:

Q: 2. Use Stokes theorem to evaluate fs da. a) a = x2 sin z da + y? dy + ry dz, S is the part of the…

A: As per our guidelines, we are supposed to answer only one question and rest can be reposted Given:…

Q: 6. Use the Normal Vector to a Smooth Parametric Surface to find the equation of the tangent plane to…

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Q: S,F•dr, and C is the triangle, with Use Stokes Theorem to evaluate where F(x,y; =) = (x+ y² )i+ (vy+…

A: Given: Fx,y,z=(x+y2)i+y+z2j+z+x2k and C is the triangle with vertices 1,0,0 ,0,1,0 and 0,0,1 We know…

Q: Use Stokes' Theorem to evaluate fF.dr if F(x,y,z) =( z-y)i +(x+z)]- (x +y)K and C is the curve of…

A:

Q: 11. Let F = (-xy + xz²)i + (4xz + y²)j + e² k. Use Stokes' Theorem to calculate fcF. dr, where C is…

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Q: Let F = < 4x + y², 5y + z, 9z + x So F. dī, Use Stokes' Theorem to evaluate C where C is the…

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Q: 3. Consider the parametric vector equation of a cone r(u, v) = u cos vi + u sin vj + uk with 1<u < 2…

A: The volume  of a cone with radius r  and height  h is given by  V=13πr2h.   Given a  function…

Q: (ii) Use Stokes' Theorem to evaluate SF · dr, where F(x, y, z) = x²zi+xy²j+z²k and C is the curve of…

A: Given function is F(x,y,z)=x2z i^+xy2 j^ +z2k^ . Plane: x+y+z=1 Cylinder: x2+y2=9 The objective is…

Q: :) Use Stokes' theorem to evaluate RF dr where C F = z?i + yj + xk and C is the triangle with…

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Q: 4) Use Stokes theorem to evaluate SF.dr, where с F(x, y, z) = <.xy, yz, *x), where C is the triangle…

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Q: r(4)=DTsin(i+ 34 j+ t°K 2. POINT: (1,2,1)

A:

Q: Let S be the portion of the plane 2x + 3y + z = 3 lying between the points (-1, 1, 2), (2, 1, -4),…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S consists of the top and the four…

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Q: Use Stokes's theorem to evaluate F.dr, where F(r, y, z) = ry i + x°yj+yz k, where C is a triangular…

A: Stroke's theorem:  ∫Fdr=∬ (Curl F) n^dS Curl F=ijkxy2x2yyzy2x2y=iz n^=∇s∥s∥=i^+k^2

Q: Use the Stokes' theorem to evaluate p Fdr where F = 3yi + yj+ :k and C is the circle r2 + y? = 3 at…

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Q: - Prove Stokes' Theorem by verifying it for F= [y,z,x] and S the paraboloid. %3D te CEY2=(x, y) = 1…

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Q: Find an equation of the tangent plane to the parametric surface. x = u + v, y=6u^2, z = u − v. at…

A: Find an equation of the tangent plane to the parametric surface. x = u + v, y=6u^2, z = u − v. at…

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

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Q: Find the work done by F in moving a particle once counterclockwise around the given curve = (2x –…

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Q: Use Stokes' Theorem to find m # 0 satisfying F · dr = -5, whereF(r,y, z) = (3yx² + z³, y², 4yx²) e C…

A: Given:

Q: 1. Identify the parametric surface S given by: r(u, v) = 3 cos ui+ vj + 3 sinu k where 0 <u < 2n and…

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Q: Use Green's theorem to calculate the work done by force F on a particle that is moving…

A: GivenF(x,y)=x32-8yi+5x+8yj,C: Boundary of a triangle with vertices (0,0), (5,0) and (0,5)To…

Q: Use Stokes's Theorem to show that 0= [[ curl(F) - dS where F(r, Y, z) = (2, 2ry, x + y) and S is the…

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Q: Use Stokes' theorem to calculate , F.ds, where F = (z, x, y) and C is the boundary %3D of a triangle…

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Q: 1. Use Stokes' Theorem to evaluate curlF.dS where F =z'i+ (4y-y) j+2zk and S is the portion of z = r…

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Q: Use Stokes' Theorem to find the circulation of F = 4yi + 2zj + 4xk around the triangle obtained by…

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Q: Use Stokes's theorem to evaluate F dr, where F(r, y, z) = ry i+x*yj+yz k, where C is a triangular…

A: Given that, F(x,y,z)=xy2i+x2yj+yzk Using the stoke's theorem, ∮F.dr=∬S(curl f.n)dS Now let's find…

Q: Use the polar coordinates to evaluate volumes : 2) Below z = V1- x2 – y2 inside x² + y2 = above the…

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Q: Use Stokes's Theorem to evaluate EF. dr. In this case, C is oriented counterclockwise as viewed from…

A: