11. Compute the surface integral (flux) of the vector field F over parametrized surface S SSFdS where S is parametrized by G(u, v)=(u+3v, v-2u, 2v+5), 0 < u < 1, 0 < v < 1, upward-pointing normal and F(x, y, z)=<-y, z,–x>

Q: 5) Consider the conservative force field F(x, y) = (6x²y? + cos(x), 4x y). a) Give a general…

A: For a vector field F=P,Q that is open and simply connected in a region with continuous first order…

Q: 4. Find the work done by the force field F (x,y) = (x + y)î + (xy)ĵ in moving a particle along the…

A: The force field is given by F→ = x+yi^+xyj^ The end points of the straight line along which the…

Q: Confirm that the force field F(, y) = 2xy°i+ 3x²y² j is conservative in some open connected region…

A: Solution:- The given function is  F(x,y)=2xy3i+3x2y2jpoint P(-9,8) and Q(6,7)we have to find the…

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: 4. Find the positively oriented flux over the surface created by the paraboloid z = 16 – x² – y2…

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Q: Confirm that the force field F(x, y) = 2xy³i + 3x²y²j is conservative in some open connected region…

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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: 9. Compute the flux of the vector field F(x, y) = (-x sin(1+xy) – 4 cos(TY), y sin(1+ xy) + 6x)…

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Q: Confirm that the force field F = xy²i + x²yj is conservative in some open connected region…

A:

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

A: According to question, G u, v = ( u + 3v, v-2u, 2v+5 ),     ........10 ≤ u≤ 1,0≤ v ≤1,Fx, y, z = -y,…

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: b) Show the force field M UTM UTM F(r, y, z) = (r²y + In(yz)) i+ UTM 3 + y cos(2z) ) j+ tial…

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Q: ind the flux of the vector field F = yzi + 7yj + yk over the sphere x2 + y2 + z2 = 4.

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Q: 3y 1. Given the vector field F(x, y, z) = · î + Vxz·ĵ+x cos y k, find curlF and div F. %3D 2. Use…

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Q: Compute the line integral of the vector field F=⟨3zy-1 ,4x,−y⟩ over the path c(t)=(et,et,t)for…

A: To Compute the line integral of the vector field F=⟨3zy-1 ,4x,−y⟩ over the path c(t)=(et,et,t)for…

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: 2) Given the vector field F = (- Vx²+y² 2z2) write the integral to calculate the outward x²+y² flux…

A: We have to find the outward flux across the cylinder x2+y2=100.

Q: 8. Show that the vector field, -y a² + y?' x² + yj²' ) is not conservative in R³, despite the fact…

A:

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

A:

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: Let S be surface of the closed region E bounded by the parabolic cylinder æ = y² and the planes z =…

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Q: Compute the line integral of the vector field F=⟨3zy−1,4x,−y⟩ over the path c(t)=(et,et,t)for −4≤t≤4…

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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 ∫F · n ds of F across the curve C for the given vector field and curve using the…

A: Solution; Consider the given function: F(x, y) = xy, x-y = P, Q P = x y Q = x -y and the boundaries…

Q: 6. Use the fundamental theorem of line integrals to evaluate 2x dr + 2y dy where C is the line…

A: Let's understand the Fundamental Theorem of Line Integrals:

Q: Compute the flux of the vector field 1 F(x, y, z) = -k x² + y2 + 1 out of the conical container K =…

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Q: 7) Consider the vector field F(x, y,z)= (y,z,x). Find the flux of this vector field across the…

A: Flux = double integral of (F(r(u,v)).ru*rv) dvdu

Q: Calculate the work done in moving a particle in the force field F = 3x2î+ (2xz-y)ĵ+ z k along a…

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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…

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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: Confirm that the force field F(x, y) = yeyi+ xey j is conservative in some open connected region…

A: We have to find the work.

Q: 2.) Calculate the curve integral over the vector field V(7, y) = ( -x*y xy² for the positive…

A: Green's theorem

Q: 2.4) Use the divergence theorem to find the outward flux of the vector field F(x, y, x) = x³i+ y³j+…

A: The divergence of the given vector field is  ∇·F=∂∂xx3+∂∂yy3+∂∂zz3=3x2+3y2+3z2 Let, S be the surface…

Q: Show that the vector field F = 2.xyi + (x – 2 y)j is conservative and evaluate the line integral %3D…

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Q: Consider the surface integral of the vector field F= [xy², 3x², x²z]over a surface S, where S…

A: From Gauss divergence theorem, we have ∬SF→⋅dS=∭VdivF→dV   The vector field is F→=xy2,3x2,x2z.…

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: 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: Consider the conservative vector field 4 8 F(x, y, z) = – 3y²cos (3nz),37y sin (3tz) – x2). 2xz, %3D…

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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

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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: 2. Determine the outward flux of the vector field F = (xy)î + (y²)ĵ over the region R depicted %3D…

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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: 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)=&lt;x-y2, y-z2, z-x2&gt; on a particle…