Compute the flux of the vector field F(x, Y, z) = 6i + 5j + 3k through the rectangular region with corners at (0,0, 1), (1,0, 1), (1,1, 1), and (0, 1,1) oriented in the positive z- %3D direction, as shown in the figure. Flux =

Q: Find the flux of the vector field F(x, y, z) = 3xi+3yj+6zk across the portion of the surface z = 25…

A: The flux F across the surface is given by ϕ=∫σF·nds=∬RF·∇GdA

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: Calculate the vector field flux leaving F(x, y, z) = xi + yj + zi solid bounded by the surfaces x² +…

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Q: Find the outward flux of the vector field F = (x³, y³, z²) across the surface of the region that is…

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Q: x²yi – x²y²j – x²yzk Calculate the net outward flux of the vector field F(x, y, z) across the…

A: Solution

Q: Calculate the flux of the vector field of (xv.z = r-)i +0= 4xz) i +xzk across the box bounded by *=y…

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Q: Find the flux of the vector field F(x, y, z) = ri across the outward oriented sphere %3D

A: In this question, we find the flux of the vector field f(x,y,z)=xi The surface is a sphere of radius…

Q: (b) Compute the flux of the vector field F(x, y, z) = y i– 2.xyk over the triangle T with vertices…

A: Given vector field is: F→=yi^-2xyk^ Given vertices of the triangle are: 1,0,0, 0,1,0 and 0,0,2 Then…

Q: Compute the flux of the vector field F(x, y, z) = 5i + 5j+ 6k through the rectangular region with…

A: Given that, The vector field F→x,y,z=5i→+5j→+6k→ through the rectangular region with corners at…

Q: Find the flux of the vector field F (x, y, z) = (e-y, -y, x sin z) across the positively oriented…

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = tan(6r + 2y + 2) . F(2, y, 2) =

A: Find the gradient vector field

Q: ind the flux of the vector field F = yzi + 7yj + yk over the sphere x2 + y2 + z2 = 4.

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Q: Find the flux of the vector field F(x, y, z) = [xy, yz, zx] through the cylinder x2+y2 <= 1, 0 <= z…

A: The given problem is to find the flux of the vector field through the given surface of the cylinder…

Q: a) Find the outward flux of the vector field F(x, y, z) = x³i+y³j + (z³ + xz)k across the surface of…

A: Concept: Divergence theorem: According to the Divergence theorem, the Surface Integral of the Normal…

Q: 6 The flux of the curl of the vector field F(x, y, z) = (y², r, 2) through the surface Σ = {(x, y,…

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

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Q: Find the net flux of the vector field F(x, y, z) = (2x, - 2y, z) over the closed surface enclosed by…

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

A: The given vector field is, F→=y, -z,  x. The given part of the plane is z=4+2x+3y And the rectangle…

Q: Compute the flux of the vector field F(x, y, z) = 6ỉ +3j + 2k through the rectangular region with…

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Q: Find the flux of the vector field F(x, y, z) = (y z, y, æz) across the surface S, where S is the…

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Q: Find the flux of the vector field F(x, y, z) = (yz, y°, xz) %3D across the surface S, where S is the…

A: Given

Q: Integrate the vector field h (x, y, =)=ry i+yz j+x k over r (1u) = ui+ j+k, -ןue-L1

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Q: Find the gradient vector field of f(r,y, z) = x*y* +y³z³ + æz°.

A: The gradient vector field of f(x,y,z) is given by ∇f=∂∂xf(x,y,z) i^+∂∂yf(x,y,z) j^+∂∂zf(x,y,z) k^…

Q: Find the flux of the vector field F(x, y, 2) = yj + k where o is the portion of the cone =' = 4(x² +…

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Q: Find the flux of the field F(x, y, z) = (x, y, -2z) through the surface z = ! =1– 2² – y² (0 < ¤< 1,…

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Q: Find the flux of the vector field F = (y, - a, z) through the helicoid with parameterization r(u, v)…

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Q: 2. Use Gauss' Theorem to compute the outward flux of the vector field F(r) = (x, y, z²) through the…

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Q: Compute the flux ∫F · n ds of F across the curve C for the given vector field and curve using the…

A: Solution; Consider the given function: F(x, y) = xy, x-y = P, Q P = x y Q = x -y and the boundaries…

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 the work done by the force field F(x, y, z) = (x − y², y - z², z - x²) on a particle that moves…

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Q: Compute the flux of the vector field 1 F(x, y, z) = -k x² + y2 + 1 out of the conical container K =…

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Q: 7) Consider the vector field F(x, y,z)= (y,z,x). Find the flux of this vector field across the…

A: Flux = double integral of (F(r(u,v)).ru*rv) dvdu

Q: Find the flux of F over the surface S of equation z2 = x2 + y2 , 0 ≤ z ≤ 3 and parameterized by x =…

A: Given:F(x, y, z) = x2 i+ y2 j+ z2k.Surface S of equation z2 = x2 + y2 , 0 ≤ z ≤ 3Let the position…

Q: Find the flux of the vector field F = 2 i +3 j – 2 k through the rectangle with corners at (1,0,0),…

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Q: A helicoid H is described by r(u, v) : (u cos(v), u sin(v), v) for 0 < u < 5 and 0 < v < 2n (with…

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Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) 5zy ze F(1, Y, 2) =

A: Gradient vector field F→(x,y,z) of a function f(x,y,z) is given by,…

Q: Compute the flux of the vector field F(x, y, z) = 3xj + 3yk through the surface S, where S is the…

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Q: The flux of the curl of the vector field F(x, y, z) = (y², x, z) through the surface E = {(x, y, z)…

A: Here first we find the curl of the given vector field using formula Curl…

Q: Compute the flux of the vector field F(x,y,z)=5xj+2yk→through the surface S, where S is the part of…

A: Flux problem...

Q: Compute the flux of the vector field F(x, y, z) = 41 + 45 + Sk through the rectangular region with…

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Q: Let o be a surface z = a – Vx2 + y² that lies above plane z=0 , oriented by an upward unit normal…

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Q: Evaluate the flux, in the specified direction, of the vector field across the surface. F(x, y, z) =…

A: To calculate the flux, we shall use the standard formula of flux in terms of the vector form of the…

Q: Sketch the vector field F(x, y) = (-x − y, x - y) at the points (x, y) where x, y = {−1,0,1}.

A: Consider the given vector field, F→x,y=-x-y,x-y Here we need to sketch the vector field at the point…

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

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Q: Consider the vector field F (x+ y)i + (x² + y²)j What is the downward flux across the line segment…

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Q: Find the flux of the vector field F = [x,y,z] through the oriented surface S: z= x^2 + y^2, z <= 1…

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Q: Compute the flux of the vector field F = zi + 8xj through the parameterized surface S oriented…

A: We have find the flux of the given vector field through the parameterized surface S oriented upward.

Q: Find the work done by the force field F(x, y, z) = (x – y², y – z², z – x2) on a particle that moves…

A: We have to find the work done by the force field F(x,y,z)=&lt;x-y2, y-z2, z-x2&gt; on a particle…

Q: Calculate the vector field flow f➝ (x,y,z) = (xy, y2, z) through the outer surface of solid T in the…

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