Answer the following questions considering the following 3D vector field F: F (x, y, z) = (x + y)(y² + z²) i + (y+ z)(x² + z²)j+ (x +z)(x² + y²) k Find the divergence of the field F. Show your manual work (i.e. do not use software) Can field F be convergent at any point? If F represents a fluid flow field, is this fluid compressible or incompressible? Which way would the particles in the fluid tend to rotate near point [-2,4,-7] in F? CW or CCW? Show your work. please

Q: Find the divergence of the field. F=(-x+8y - 3z)i+ (8x- 4y + 3z)j+ (- 4x- y- 3z)k

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Q: If F =  P i + Q j + R k is a vector field on R  3  and aP/ax , aq/ay and  ar/az exist, hen the…

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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: The vector field F is shown in the xy plane. 1 2 Is div F positive, negative, or zero? Positive…

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Q: 3. Let F be the vector field (ze"z + yz², xz², xe™z + 2xyz) (a) Find the divergence of F.

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Q: Find a vector field with twice-di£erentiable components whosecurl is x i + yj + z k or prove that no…

A: To find: The vector field with twice differentiable components whose curl is xi+yj+zk, prove that no…

Q: 2) For the vector field F(x, y, z)=(xz²-x²y)i + (xy²-y³2²)] +xy²z³k, find the following: a) Find the…

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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: Calculate the divergence of the vector field F=x²y³z¹i-xyzj+(x+y+z) k

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Q: Evaluate both sides of the divergence theorem for the vector field D = 2xyx + x²9 [C/m²] and a…

A: This question is belong to the vector calculus in which we have to deal with the divergence theorem…

Q: Consider the following vector field. F(x, y, 2) = (4e* sin(y), 9e' sin(2), 8e" sin(x) (a) Find the…

A: Solve the following

Q: find the divergence of the field. F = (x - y + z)i + (2x + y - z)j + (3x + 2y - 2z)k

A: Given Data The field function is fx=x-y+zi+2x+y-zj+3x+2y-2zk.   The expression for the divergence of…

Q: 4. (a) Show that the divergence theorem holds for the vector field F = 2xî + yz} – 3z²k where o is…

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Q: 1. Give an example of a vector field F(x, y) in 2-space such that F has constant direction but || F…

A: The solution are next step

Q: Find the divergence of the field. F= (4x + 5y + 7z)i + (8x - 8y + 3z)j + (2x - 7y + 4z)k div F =

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Q: For a force field F, if curl F= 0, then the field is nonconservative field. True False

A: False

Q: 10. Evaluate the divergence of the following vector field at the point (0,1,2): F = (xyz, x? + y? +…

A: Given: F=xyz,x2+y2+z2, xy+yz+xz       The point 0,1,2 To find the divergence

Q: 3. Find the divergence of the vector field. F = ye2* i+2 ye³j 2.x²

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Q: Determine whether the following vector field is conservative on R. F-(2 + 3xy 3y +2y) Is F-(2x + 3xy…

A: Explanation of the answer is as follows

Q: Q4// A// Evaluate both side of divergence theorem for the field D=2xy.x^+x².y^ C/m2 and the…

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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: (a) Are the points P1  and P2 sources or sinks for the vector field F shown in the figure? Give an…

A: Part (a)

Q: Which of the following statements is correct ( where F is a continuouslydifferentiable vector field…

A: Given: Which of the following statements is correct ( where F is a continuously differentiable…

Q: 3. Find a field F(x,y) = (M(x, y), N(x, y)) in the xy-plane with the property that at each point

A: Let f = xi + yj  Then F = ff = unit vector = xi+yjx2+y2

Q: find the divergence of the field. F = (yexyz)i + (ze xyz)j + (xexyz)k

A: Given  F=(yexyz)i→+(zexyz)j→+(xexyz)k→ To find the divergence of the field If F=Pi→+Qj→+Rk→, the…

Q: find the divergence of the field. 1. F = (x - y + z)i + (2x + y - z)j + (3x + 2y - 2z)k 2. F = (x ln…

A: Consider the vector field Substitute the value of vector fields then Hence, the divergence of…

Q: Find the divergence of the field F. F = 8x 5 i + 3y 5 j + 2z 5 k 8x4 + 3y4 + 2z4 O 40x4 + 15y4 +…

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Q: Consider the vector field F = ( 'x²+y2 'x²+y2/ Write yes or no for each: Is this field conservative…

A: The solution are next step

Q: Find the divergence of the vector field F. F(x, y) = 7XEX¡ – 9x²y2j

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Q: Find the work done by the three-dimensional inverse-square field F(r) : 1 r on a particle that moves…

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Q: What is the divergence of the vector field F of F(x,y) = x² i + 2y²j?2 div F = 2x + 4y div F = 4x +…

A: Given: F→=x2i+2y2j

Q: 6. Find the circulation of the field F(x, y) = -yi + x²j along the closed elliptical path x² + = 1…

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Q: Find the divergence of the following vector field: 00 O 2z O F = (y, -x + z², 3x)

A: We can solve this as follows:

Q: 3. Find a field F(r,y) (M(r, y), N(r, y)) in the xy-plane with the property that at each point (r.…

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Q: Find the divergence of the field. F = (- 6x + 8y – 4z)i + (- 8x – 5y + 3z)j+ (x + 5y + 2z)k div F =

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Q: Find the divergence of the following vector field. (x.y.z) F= 6+ 4x + 3y 2 The divergence of F is

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Q: Find the divergence of the following vector field. F = (2x?yz, - 2xy²z, - xyz²) The divergence of F…

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Q: Consider the following vector field. F(x, y, z) = xy²z²1 + x²yz²j + x?y²zk (a) Find the curl of the…

A: div F = i∂∂x+j∂∂y+k∂∂zF(x,y,z) curl F = ∇×F

Q: Which of the following is the divergence of the vector field F=x,y,z)? none of these 3. -3

A: The correct option is 3rd option .i.e. 3 .

Q: Find the divergence of the field. F= 5z e 8xyz i+ 5x e 8xyzj + 5x e 8xyZk div F=O

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Q: Consider the following vector field. F(x, y, z) = xy²z²i + x²yz²j + x?y²zk (a) Find the curl of the…

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Q: 13. Calculate the divergence of the vector field F = x1e1 + 2x1e2 + +nx1en. ...

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Q: Find the divergence of the following vector field. F= (3xyz, - 2xy z, - 4xyz?) %3D The divergence of…

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Q: Define the following :- i) Vector Field. #) Piecewise Smooth Curve C

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Q: Evaluate the divergence of the following vector field at the point (1,1,1): F= . Select one: O 5 1 3…

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Q: (a) Are the points P1 and P2 sources or sinks for the vector field F shown in the figure? Give an…

A: (a) Are the points P1 and P2 sources or sinks for the vector field F shown in the figure? Give an…

Q: Determine whether the following vector field is conservative on R. F- (x.4y)

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Q: Evaluate the divergence of the following vector field at the point (1,1,1): F = . Select one: 3 7…

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Q: 1. For the scalar field 0 = x3 + 2xy in the domain ABC below, calculate the gradient field and then…

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