11. Compute the surface integral (flux) of the vector field F over parametrized surface S S where S is parametrized by G(u, v)=(u+3v, v–2u, 2v+5), 0

Q: 5. Consider the vector field F(x,y,z) = yzi + xzj+(xy+2z) k and the curve C given by r(t) = (t+ sin…

A: Given vector field: Fx,y,z=yzi+xzj+xy+2zk Curve C is given by: rt=t+sin12πt,t+cos12πt,2t,   0≤t≤1…

Q: The potential of the conservative vector field F = (y,x,1> is Of=z+xy O f=x+yz O f=y+xz Of = xyz

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Q: Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface…

A: Here we will use Stokes theorem  to calculate  flux of curl (F) on surface S bounded by curve C…

Q: Consider the conservative vector field 8 4 F(x, y, z) = - 2xz, - 3y²cos(3nz), 3ny sin(3nz) – x² ) 2х…

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Q: Q3) Compute the work done by the force field F(x,y,z) = (3x, xz, y) on the curve C, where C is the…

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Q: 1- Prove that the force field F known as : Prove that the force field defined by F = (y*z' -6xz? )i…

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Q: From the given vector field F⃗ (x, y, z) = , compute the curl of F⃗ and find the values of a and b…

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Q: 1. Consider the vector field F(x, y, z) = (2e2" cos(3y), –3e²" sin(3y) + Y a. Find divF(x, y, z) and…

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Q: I. Use the Divergence Theorem: (² F. ds = Ifv. Fav SSS E = to calculate the flux of the field F…

A: Divergence theorem uses  Double integration converts into triple integration.

Q: 10.) Use the Fundamental Theorem for Line Integrals to find the work done by the conservative vector…

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Q: 8. Given the vector field G(x, y, z) = e>+2z (1 + x j + 2xk) : a) Show G(x, y, z) is conservative…

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Q: Evaluate the line integral F. dr, with vector field F(x, y, z) = sin xi + cos yj + xz k, and path C…

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Q: 2. Calculate the directional derivative of the scalar field U(x, y,z) at the point M,, along the…

A: Given that : U=xz3y-x3y=xz3y-x32y12 The gradient will be calculated as :…

Q: Evaluate line integral of vector field F(z,9) = i+ 1- x? y2 2x along the curve x = cos(t), y =…

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Q: 3. Consider the vector field F = 2xy i + (x² + 2y) j. Verify the Green's Theorem in the closed…

A: Definition of green's theorem :

Q: 5) Find the work done by the force field F(r, y, z) = ri-zj+y k in moving an object along the…

A: Work = Force X Displacement

Q: 10. [ Find the flux of the vector field F(x, y, z)= 3 over the surface S, where S is the surface of…

A: The general form of a vector-valued function in three dimensions is given by F→=Fx, Fy, Fz, where…

Q: The circuitation of the vector field F(x, y)- (3 + xy´, 4x + xy) along the boundary of the plane…

A: The solution are next step

Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = Jx2 + y2 + 3 that…

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Q: Determine whether the vector field…

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Q: 6 The flux of the curl of the vector field F(x, y, z) = (y², x, z) through the surface = {{x, y, z)…

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Q: Find a potential function for the conservative vector field given by y3/2 2T 2 2x sin z F(r, y, 2) =…

A: We will find out the required potential function.

Q: Compute the flux of the vector field F 3yi + 4j – 3xzk through the surface S, which is the surface y…

A: We apply formula for finding this

Q: Suppose that v = (0, y, 0) is the velocity field of a fluid and let S be the surface defined by y =…

A: Given, the velocity field v→=0, y, 0and S be the surface defined by y=x2+z2, with y≤1.

Q: 4. Evaluate the line integral Vf-r'dt, where the curve C is given by the vector function r(1)…

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Q: In(t) i + t312j + t cos(at)k, F. dr of vector field F(x, y, z) = 3x²zi + zj + (x³ + 2yz)k along…

A:

Q: Given that the vector field F(x, y) = (2x-3y, 2y-3x) is conservative in the xy-plane. If (x, y) is a…

A: We have to find the value

Q: 1.) Given the conservative vector field F(x,y,z) = ( y In z,x In z, xy find the work required to…

A: The conservative vector field Fx,y,z=y ln z, x ln z, xyz. The parametric equation of line segment…

Q: Find line integral fF. dr of conservative vector field F (x, y, z) = 'i+ j+-k where C is a path from…

A: Find the line integral of a conservative vector field

Q: 4. (a) Show that the outward flux of the postion vector field F(x,y,z) = (x)7+ (y)] + (z) through a…

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Q: Find all potential functions of the conservative vector field F (x, y, z) = (2xz + y², 2xy,x² + %3D…

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Q: Find the total flux of the field x+ /1+ y² + z² 2y + V1+x²+ z² \3z + /1+x² + y², F(x,y, z) = out of…

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Q: I have trouble getting to the answer. Just wondering if I can get it step by step.

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Q: (10) Given that the vector field F= 2z i- 3 x j + 4 y k Evaluate f F. dr where S is the portion of…

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Q: If F = xy i+ (x² + 4yz)j+ 2y²z k. Evaluate the line integral between A (0, 2, 0) and B (3, 6, 1).…

A: Given, F= xy i +(x²+4yz)j +2y²zk r0= (0,2,0) r1= (3,6,1)

Q: 11. Compute the surface integral (flux) of the vector field F over parametrized surface S SSFdS…

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Q: Consider again the vector field F = (x + y)i + (x² + y² )j. What is the downward flux across the…

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Q: Show that the vector field F = 2.xyi +(x² – 2 y)j is conservative and evaluate the line integral…

A: Given the vector field

Q: Choose from the list below the velocity field corresponding to the motion of an incompressible…

A: Given velocity fields, v(x,t)=x1x2,0,x2x3Tv(x,t)=x1x3,-x2x3,0Tv(x,t)=x1x2,-x2x3,0T The objective is…

Q: 2) Given that the total flux across the surface, S of the tetrahedron bounded by the planes x = 0, y…

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Q: 10. Use the Divergence Theorem and the vector field F = to compute the outward flux from the region…

A: Here we will evaluate the outward flux.

Q: F(x, y, 2) = (y² cos r + 2*)i+ (2y sin æ – 4)j+ (3xz² + 2)k Cos z

A:

Q: 16. Compute the flux V· nds of the vector field V(r, y) = (x² – 2ry, y² – 2xy) across the curve C :…

A: We have to compute the flux ∫ℂV·nds of the vector field Vx,y=x2-2xy,y2-2xy across the curve…

Q: Suppose that S is the boundary surface of the solid region B that is bounded by the paraboloid z =…

A: Given vector field F→x,y,z=2zey+xy2i→+xz2-2zexj→+x2z+2xe-yk→. To find the flux of the vector field…

Q: 12. Find the flux of the field F(x, y, z) = 4xi + 4yj + 2k outward (away from z-axis) through the…

A: Flux of the given field is given by

Q: Compute the flux of the vector field F = zi + 8xj through the parameterized surface S oriented…

A: We have find the flux of the given vector field through the parameterized surface S oriented upward.

Q: Consider the one-form w = x' cos(y) dx + xe13% dy+4z² dz on R3. The associated vector field is: F(x,…

A: For the solution follow the next step.

Q: Find the flow of the velocity field F = b. a. Na g (2,8) : 4x (0,0) X (5y² + 1)i + (10xy)j along…

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Q: a) What is the flux of the constant vector field F = (a, b, c) through any closed surface? b) Is the…

A: Given That : A constant  vector field F=a,b,c and F=x3,y3,z3 To Find : i) The Flux through of…

Q: Find the work done by the force field F(x, y, z) = (x – y², y – z², z – x2) on a particle that moves…

A: We have to find the work done by the force field F(x,y,z)=<x-y2, y-z2, z-x2> on a particle…