Find the divergence and the curl of the vector field . F(x,y,z)=1/√(x^2+y^2+z^2 )(xi+yj+zk)

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: Compute the curl and divergence of the vector field F(x, y, z) = (T 2², 2yz) . Is F conservative? If…

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Q: Find the flux of the vector field F = (y, z, x) across the part of the plane z = 4+ x + 3y above the…

A: The surface integrals compute the flux of fields across surfaces,                   So,…

Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 4 + x + 2y above…

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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: F = (x² +y², y² +z?,.

A: on solving this we get the

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

A: We will find out the required value.

Q: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

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

A: step 2 complete solution

Q: Find the divergence and the curl of the vector field F(x, y, z) = x²yi + 2y'zj+3zk

A: The vector field given is : F(x,y,z) = x2y i +2y3z j + 3z k

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: Determine the line integral if the vector field is F(x, y) = x²yî – 2xyf On a rectilinear path that…

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Q: Use the divergence theorem to calculate the flux of the vector field F = x3i - 3x2yj + 6zk through…

A: The divergence theorem is defined by the formula, ϕ=∮∂VF·ndS=∮V∇·FdV Consider the given vector…

Q: FIND THE DIVERGENCE OF THE VECTOR F GIVEN = sin (8x)i + cos (5y); + z ² k FIELD F(X, Y, 2) BY

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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: Find the divergence of the vector field F→(x,y,z)=7sinxi→−cos(3y)j→+z^9k→.   Enter the exact…

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Q: Find the divergence of the vector field F = < yx², xzª, zy³ div F =

A: f = y x2  ∂f/ ∂x = 2xy   g = x z4  ∂g/ ∂y = 0   h = z y3  ∂h/ ∂z = y3

Q: Find the divergence of the vector field At the point (2,4,1). F(x, y, z)=x²2√√yi + -j + zk

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Q: the gradient vector field of f(z, y) = In(x + 4y) %3D Work

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Q: Calculate the integral line of vector field F(x,y) around the circle x²+y²=1 oriented…

A: Given that Fx,y=-2yx2+y24+2x,2xx2+y2/4+xy+1. The the integral line of vector field F(x,y) around the…

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = In(x + 3y + 4z) . F(2, y, 2) =

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Q: Find curl F for the vector field at the point (9, -9, 5). F(x,y,z) = x²zi - 2xzj + yzk curl F =

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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: 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: Find the curl of the vector field F. F(x, Y, 2) = arcsin yi+ V1 - xzj + yêu y²k

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (7, -9, 5)…

A: Concept:

Q: Find the divergence of the vector field F = < ya", xz°, zy* div F

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Q: Find the flux of the vector field F = (y, – z, x) across the 2 + 4x + 3y above the rectangle part of…

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

Q: Compute the work done by the vector field F(x, y) = (ry, x² + y³) when moving a particle…

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Q: 9) Find the (i) divergence and (ii) curl of the vector field F(2, y, 2) = (4yz) i+ (y²z) j + (ryz) k

A: We have to find curl

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: Find the divergence at (15, 0, 0) for the vector field F(x, y, z)= e*sinyi-e cosyj+z²k O 16 O 451 30…

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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: 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 at the given point. F(x, y, z) = xyzi + xz²j + 4yz²k; (3,…

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Q: The divergence of a vector field F = 3x² yz? î + 2yz ĵ – xz² k at he point (1,0, 1) is -2 O 2 O 1

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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: Compute the outward flux of the vector field F = (5xy, 5y²) for the region enclosed by the curves y…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Compute the curl of the vector field F = 2y3 i+ e j+ cos(x) k curl

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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: Find the divergence of the vector field V(x, y, z) = -2e*'i – e³xyj+ 7e%yzk.

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Q: Compute the flux of the vector field F = 2xi + 2yj through the surface S, which is the part of the…

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Q: Calculate of A= Xzi- 2x*yzj+2yz'K at ( 1,-1,2). the Curl and Divergence

A: Given A = xz3i-2x2yzj+2yz4k Compare it with A = Axi+Ayj+Azk Hence Ax = xz3Ay = -2x2yzAz = 2yz4 Then…

Q: Find the divergence of the vector field of F(x,y,z) = sinxi + cosy j + z² k. cos x + sin y + 2z O…

A: Option C is correct. To finde divergence I used divergence formula.

Q: B) Find the work done by the conservative vector field F (x, y, z) = yzi+xzj+xyk along a smooth…

A: Since, it is given that the field is conservative.