Which of the following cannot be a conservative vector field? O H) None of these C) F = ( z In y,,x In y ZX - y - F) B and E G) A, B , and D o A) = (yz, xz, xy) E) zy F = 3 , Xzy*, V1+ zy* - D) F=cos (x² + y +z)(2x,1,1) + y+z

Q: Show that the vector field F(x, y, z) = xz i + xyz j - y 2 k can’t be written as the curl of another…

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Q: Compute the circulation of the vector field F=(4cos(y))i+(3x^2sin(y))j around C. Where C is the…

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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: Assume that Ax, y, z) is a vector field whose i component is only in terms of y and z, whose j…

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Q: A vector field is given by V = (5x²+4y)į + 5y²j + (z² + 3)k, using Gauss's theorem (or Divergence…

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Q: 2) If F(x, y, z) = x²i + y²j + 3zk is a vector field, use Divergence theorem to calculate the…

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Q: Compute the flux of the vector field F 3.ri + 3yj through the cylindrice surface shown below, if a=3…

A: To calculate the flux of the vector field.

Q: Give an example of a vector field F(z, y) in 2-space with the properties that F is perpendicular to…

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Q: A vector field is described as F = (-z + 7x, x³y²z=1,3x + 2z²). (i) Calculate curl F. (ii) Determine…

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Q: 4. Is the vector field F(r, y, :) = (yz,rz, ry) conservative? Justify your answer.

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Q: If a vector field F (x, y, z) = (evz-, In (x² z), sin z), which of the following values is equal to…

A: We have to find div F(-1,0,1).

Q: Could the following vector field. F. be conservative F(z,9) = (6z" cos (y), 4y²cos (z)) Select the…

A: Given vector field Fx,y = 6x4 cos(y), 4y3 cos(x)

Q: 3. Use the Divergence Theorem to find the flux of the vector field F = (5x+ 4y?z – 162³) i +…

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Q: . Consider the vector field F(r, y, 2) = (8r sin y, 4x² cos y – e"z, -e" – sec² z). %3D | F. dR…

A: For a vector field F→, the line integral about the path C is ∫CF→·dr. Let rt be the parametric…

Q: 7. Consider vector field F(x, y, z) =. (а) Show that F(x, y, z) is irrotational, i.e., that V x F…

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Q: What is the divergence of the vector field f = x²i+ xyzj – zk at the point (1, 2, 3). Select one: а.…

A: f=x2i+xyz j-zK at (1,2,3)  div f=i ∂f∂x+j.∂f∂y+K.∂f∂z

Q: A smooth vector field F has div F(2, 5, 5) = 2. Estimate the flux of F out of a small sphere of…

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Q: (a) Show that the vector field F (x, y, z) = (x² + y², x, z³) is not conservative.

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Q: 3. Verify the circulation form of Green's Theorem for the vector field F(x,y)=xyi +2y and the region…

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

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Q: (5) Compute the vector Surface integral of the {x,y,Z> vector field F(x.y,z)= A_r = A F = A IF3…

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Q: Determine whether the following vector field is conservative on an open region R of R2 that does not…

A: For our guidelines answer only  question 2 but I give answer of both questions

Q: Given the vector field F(x,y,z) = [x, y, -2z] satisfies div(F) = 0. Find a vector field G(x,y,z)…

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Q: A vector field with component form F(x, y, z) = (P(x, y, z), Q(x, y, 2), R(x, y, z)) on R³ is…

A: Given that Fx,y,z=excosy,e-xsiny,2 The objective is to show that F is conservative. So to show that…

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: Is there a vector field G on IR such that curl G = (xyz, -y°z®, y8z®)? O Yes O No Explain. There…

A: Given

Q: Show that the following vector field is conservative and find the potential F(r, y, z) = (2ry, x² +…

A: The answer is given as follows.

Q: Find the divergence of the vector field F. F(x, Y, z) = In( 9x²+ 8y² )i + 72xyj + In(8y² + 7z? )«…

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Q: (b) Verify Green's Theorem for a vector field F(x,y) = xy²i – yx²j on a disc with center (0,0) and…

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Q: Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x² +…

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Q: Use the extended divergence theorem to compute the total flux of the vector field F(x, y, 2) 3D…

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Q: Let F be the vector field (x², 2r, 2²). Let C be the boundary of Lv **---- the surface S given by…

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Q: Find the divergence of the vector field F. F(x, y, z) = In 5x²+ + 10xyj + In( 2y2 + 722)k div F(x,…

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Q: There is a vector field F (, y, z) such that divF (x, y, z) = curlF (x,y, z). (M (x, y, z) , N (x,…

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Q: Find a vector field with twice-differentiable components whose curl is x i + yj + z k or prove that…

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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 vector field F(x,y,z)=(−3x^2,8(x+y)^2,9(x+y+z)^2). Find the divergence and curl of FF.…

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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: 6. Show that F = [y? cos x + z3, 2y sin x – 4, 3xz2 + 2] is a conservative force field. Find the…

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Q: Show that Green's Theorem holds for the vector field F(x, y)=(x +y, 3x) at a square of side 2.

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Q: Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous…

A: Given: The vector field F=Pi+Qj+Rk is conservative P, Q, R have continuous first order partial…

Q: 4- Evaluate the surface integral of the vector field F = = [ax, by, cz] over the sphere a2 + y² + z²…

A: From the given problem:   F→=axi+byj+czk   Sphere:  x2+y2+z2=36.   From the divergence theorem:…

Q: Let C be the curve of intersection of z = 1 – 2x2 and the cylinder x2 + y2 = 1 oriented…

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Q: the vector field F is shown in the xy plane. y 21 2 Is div F positive, negative, or zero? Positive…

A: Given : The vector field F is shown in the xy plane :   We have to determine that : Is div F…

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

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Q: (7) Verify the Divergence Theorem for the vector field F = azi + yzj +32²k defined in the solid…

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Q: "roblem #5: Use the divergence theorem to find the outward flux F.n dS of the vector field F =…

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Q: : Verify the divergence theorem for A=4xi +(2Y+z Vector field ) | +(52-2x)k in the regim beunded by…

A: According to the given information, it is required to verify the divergence theorem for a vector…