Find the divergence of the field F. F = 8x 5 i + 3y 5 j + 2z 5 k 8x4 + 3y4 + 2z4 O 40x4 + 15y4 + 10z4 65

Q: The vector field F is shown in the xy plane. 3- 2- 2 3 4 Is div F positive, negative, or zero?…

A: Divergence is a operator which operate on vector field F to gives a scalar quantity . And divF is…

Q: Consider a field with V = 8a²y² î + 4y²j + –5y² z³k a) Find the divergence of V: V•V: b) Find the…

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Q: Find the divergence of the field F. F = 8x 5 i + 3y 5 j + 2z 5 k   a) 65   b) 8x4 + 3y4 + 2z4…

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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: Find the potential function f for the field F. F= (4x3y10z10, 10x4y9z10 10x4y1029) O fix, y. 2) =…

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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: What is the divergence of the vector field f=3x i+5xy j+xyz'k at the point (1, 2, 3). Select one: а.…

A: Solution:-The given vector  field is Step:-1    f=3x2i+5xy2j∧+xyz2k∧  then,  we have  to find the…

Q: For which value of a the field i = (y –x)i +(2x – y)j + azk is solenoidal. Find the gradient of the…

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Q: find the work done by each field along thepaths from (0, 0, 0) to (1, 1, 1) in Exercise 1.F = 2xy i…

A: Given: F=2xyi+j+x2k To Find: Find the work done by each field along the paths from 0,0,0 to 1,1,1.…

Q: Q4 A) Calculate the divergence of the vector field F=y³i + xyj B) Find the Curl of F(xy.z)=3x²i +…

A: To find out the divergence of vector field.

Q: Find the divergence of the vector field F. F(x, y) = 8xe*i – 7x²y²j |

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

A: r(t)=<6,2,3>+t<2-6, 6-2, 9-3> r(t)=<6-4t, 2+4t, 3+6t> r'(t)=<-4, 4, 6>…

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: 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: Find the divergence in (2,1,-1) for the vector field FCX₁Y₁² ) = x³y² 2 ² + x ² z 3 + x^²yk

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

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Q: a) Find the curl and the divergence of the vector field: F = (3x + 2z?)i + (*)j- (2- 7x)R.

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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: Q2. (a) Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k. (i) Determine whether if F is…

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Q: 14. Find the curl of the vector field F = x²i – xevj+ 2xyzk

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Q: F(x.y) = (4xy, - 3y²> A V.F- 4x B VF-1 © v.F = 4x - 6y (D vi--2y

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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 div ccurl F) = v(♡XFJ For the V cetor Field given By F(AoyoZ)= X=i -6xzj + yz K

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

A: Solution

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: Q2 A) for F= 2xi-3Y3+K %3D prove That div( curl È)=0

A: Given :          F→ = 2x i - 3y j + k   To prove that div(curl F→ ) = 0

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: Determine whether the following vector field is conservative on R°. If so, determine the potential…

A: We have to solve

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: (a) For any vector field F, the gradient of the divergence of F is always zero.

A: Since the gradient of divergence of F is given by

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: (b) Find the scalar potential of the conservative field: F = 2ry°z?i + 3x²z²y²j+ 2x?y³zk. %3D

A: Let's find.

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

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

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Q: Find the divergence of the field F. yj - xk F= 1/2 +: 2 OA. 3/2 2 -X O B. 3/2 2 X -y OC. 3/2 O D. 0

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Q: Find the potential function f for the field F = 6xi + 6yj + 4zk. %3D

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Q: find the divergence of the field. 1.F = ye^(xyz)i + ze^(xyz)j + xe^(xyz)k 2. F = sin (xy) i + cos…

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Q: Find the divergence of the field. 2xyzk F = 5ye 2xyzi + 5z e 2xyzj+5x e² div F =

A: Solve the following

Q: Q5: a) Show that the vector field F = (x² - y² + x)i - (2xy + y)j, is irrational.

A: Given vector field is F→=x2-y2+xi^-2xy+yj^. To show: Vector field F→=x2-y2+xi^-2xy+yj^ is…

Q: Q5. (a) Show that the curl of F is the vector field VxF=i-j-k

A: answer is in next step . please give a like .

Q: Define the followings. 1. curl F, the curl of the vector field F = Pi + Qj+ Rk. 2. div F, the…

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Q: If the scalar field is given by f = 2p², the result of V × Vƒ at P(4, ,4) 3

A: The expression for the gradient in the cylindrical coordinates  is given as . Following are the dot…

Q: Find the gradient field of the function f(x.y.z) = In 4x + 4y2 +z?. ..... The gradient field is Vf=…

A: Gradient of F is given by

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

A: Solution :-

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

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