Find the divergence of the vector field F→(x,y,z)=xyzi→−yzj→+xzk→at the point (8,3,2) .   Enter the exact answer.   divF→(8,3,2)=

Q: Compute the upward flux of the vector field Ĥ(x, y, z) = (x, 0, 2z) across the portion of the…

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Q: Determine the divergence of vector field E = 3x²x + 2zŷ + x²z2 at (2, –4, 0).

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Q: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…

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Q: If ϕ=3xy+2x2yz−12xz3ϕ=3xy+2x2yz−12xz3, Find ∇×(∇ϕ)

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

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Q: Compute the work done by the vector field F(x, y, z) = (,2, 2yz) when moving a particle: 1+? > a)…

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Q: Find the divergence of the vector field F = < yx®, xy®

A: Given,         The vector field is F¯=&lt;yx3 , xy6&gt; .

Q: Find a potential for the conservative vector field: F(x, y, z) = (2xy + 2x, x² – 2yz³, –6z – 32²y²)…

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Q: What is the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

A: We find the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

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: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6) O…

A: To find the curl for the vector field  at the given point.Fx, y, z=6xyzi+6yj+6zkPoint=6, 7, 6

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: Choose a correct potential function for the conservative vector fieldF = (3x-y+1, –x-4y-2).

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Q: Find the flux of the vector field F = (y, – z, x) - 2, - across the part of the plane z = 2 + 3x +…

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Q: Find the conservative vector field for the potential function by finding its gradient. 9 (r,y, 2) =…

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Q: Is there a vector field Ğ on R³ such that curl Ġ = (xyz,–y*z³,y*z*)?

A: the given function is, G→=xyzi^-y4z3j^+y3z4k^ If there exists a vector field G then the divergence…

Q: Verify the Divergence Theorem in the calculation of the flux of the vector field: through the…

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

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Q: Compute the flux of the vector field (x, (æ°, – ay*), out of the rectangle with vertices (0,0),…

A: To compute the flux of the vector field x3,-xy4, out of the rectanglewith vertices 0,0,2,0,2,4…

Q: Find the divergence of the vector field. V(x, y, z) = 4yzi + 6xzj + xyk div(V) =

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Q: Show that the vector field F=2xyi +(x -2y)j is conservative and evaluate the line integral |F•ds…

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Q: Find the work W done by the vector field ⟨2x+yx,x2+4⟩ on a particle moving along the boundary of the…

A: To find the workdone by the vector field.

Q: Graph the vector field F(x, y)=(-3y, 2x); also find the divergence and the rotational.

A: The graph of the  vector field F=-3y, 2x is as follows

Q: Find a potential functioon for the conservative vector field given by y3/2 3 xy + z, 2 sin z 2.x…

A: According to question,Given vector field,F→x, y, z = 2xx2 + cos z-y322x, -32xy+z, -sin zx2 + cos z+y

Q: Find the curl of the vector field F(x,y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Let the given vector field is :

Q: compute dr for the vector field where Cis the line segment from Co.o) to Cli3)

A: Given vector field is, F=1+x2,xy2  The objective is to compute ∫CF·dr, where C is the line segment…

Q: Find the divergence of the given vector field at point (1,1,1). Insert your answer below. Round to…

A: Fx, y, z=3x2yi+2xz3j+y4k Comparing with F=Pi+Qj+Rk, we get P=3x2y,  Q=2xz3,  R=y4 Now, ∂P∂x=∂3x2y∂x,…

Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 3yz²k; (2,…

A: This question is based on divergence of vector.

Q: Find the gradient vector field (F(r, Y, 2)) of f(x, y, z) = In(4x + 6y + 22) . F(7, y, 2) = (

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Q: Find the curl and the divergence of the vector field. F(x, y, z) = x²yzi - x³y k i + Submit Answer…

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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: Show that the vector field =(-2 x²y xy²¹ is conservative by finding all its potential functions.…

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Q: Find the divergence of the vector field. V(x, y, z) = 7e*Yj – 9e*Yj + 8EY²K - div(V) II

A: A detailed solution is given below.

Q: Find the divergence of the vector field F. F(x, y, z) = In( 7x²+ 4y² )i + 28xyj + In( 4y2 + 5z2 )k

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Q: Find the flux of the vector field F = across the part of the plane | z = 2 + x + 3y above the…

A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…

Q: 3. Find a potential for the conservative vector field: F(x, y, z) = (2xy + 2x, x² – 2yz³, -6z –…

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Q: Find the curl of the vectòr field F(x, y, z) = 2xyzi + 8yzj + 5zk

A: According to our guidelines we are supposed to do only one question.  Kindly repost other question…

Q: Use the Divergence Theorem to find the flux of the vector field F = (3x2 – 3yz + 423) i + (4.xz –…

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Q: How much work is required to move an object in the vector field given as F = yi+3x j Along the lower…

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Q: Calculate the divergence and the curi of the following vector field at the point (1. 2. 1) Fix, y,…

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Q: Find the divergence of the vector field F = < yx², xz", zy® div F II

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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: Consider the curve C from (-2, 0, 1) to (6, 5, 2) and the conservative vector field F(x, y, z) =…

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Q: If the vector field A = âx3x² + âyy – â̟5z³ is given, express à in cylindrical and spherical…

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Q: Find a vector potential field for Ġ = [6xz+x³, –3r²y – y², 4.x + 2zy – 32²], i.e. find F such that V…

A: The solution is below.

Q: Calculate F=, around the triangle with vertices: (0,0,2), (2,0,0) and (0,2,0). Can you use Stoke's…

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Q: Let F(x, y, z) =⟨3x2y+az, x3,3x+ 3z2⟩ be a vector field. For what values of a is F conservative?

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Q: Find the divergence of the vector field F %3D div F =

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Q: Q3 Show that the vector field F= 2xyi +(x -2y)j is conservative and evaluate the line integral |F•ds…

A: Solution

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj+yzk; (9,-9, 9) curl F…

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