Find the net outward flux of F = a x r across any smoothclosed surface in ℝ3, where a is a constant nonzero vector andr = ⟨x, y, z⟩ .

Q: Use the divergence theorem to calculate the flux of the vector field F(x,y, z) = 2xyi + z8 j + 6yk…

A: Divergence Theorem:      ∬F→·dA→    = ∬∫∇·F→dv       s                       v

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = 5xyi + z°j+9yk…

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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: Compute the flux of vector field V = .2 x +y2 x +y2 across the surface of the ellipsoid x2 y?, z2 +…

A: Divergence theorem establishes the relationship between line integral of vector field and the volume…

Q: Find the flux of the vector fielol F from the baunelries of the given region (o). 37 2. (D): solid…

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Q: Exercise: 5 a) Find the outward flux of the vector field F(x, y, z) = x³i + y³j + (z³ + xz)k across…

A: Given the vector field  Fx,y,z=x3i+y3j+z3+xzk and z=a2-x2-y2

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 flux of the vector fleldF = (x – y*)i+ 4yj + x'k out of the rectangular solid [0, 1] x [1,…

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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: Find the flux of the vector field V(x, y, z) = 6xy²i + 7x<yj + z°k out of the unit sphere.

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Q: Exercise: 5 a) Find the outward flux of the vector field F(x, y, z) = x³i + y³j+(z³ + xz)k across…

A: To find the outward flux of the vector field Fx,y,z=x3i+y3j+z3+xzk across the surface of the region…

Q: Exercise: 5 a) Find the outward flux of the vector field F(x, y, z) = x³i+y³j + (z³ + xz)k across…

A: a) find the outward flux of the vector field Fx,y,z=x3i+y3j+z3+xzk across the surface of the region…

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

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Q: Compute the net outward flux of the vector field F = (x i + y j + z k)/ (x2 + y2 + z2)^(3/2) across…

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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…

A: Outward flux by using gauss divergence theorem

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: calculate the flux of the vector field through the given surface. ~F = ~i + 2x~j + 4y ~k, and S is…

A: GIVEN: F = i + 2xj + 4yk Surface, z = 2x2 + y + 3

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x°i + (5y – 5x*y)j…

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Q: Show that the vector field F (x, y, z) = xz i + xyz j y 2 k is not conservative.

A: Consider the following vector: Fx,y,z=xzi^+xyzj^+y2k^ Find the Curl of F→:…

Q: Use the Divergence Theorem to find the outward flux of the vector field F(x, y, z) = 7x3i +…

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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: Calculate the flux of the vector field (x°, y), out of the annular region between the a + y? = 16…

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Q: Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = xy2i + yz2j +…

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Q: Calculate the flux of the vector field (x, y³), out of the annular region between the x? + y? = 1…

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

A: The vector field given is as follows: Fx, y, z=x3i^+y3j^+z3+xzk^ We are asked to find the outward…

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

A: Let E be a three-dimensional solid bounded by a piecewise smooth closed surface S that has…

Q: Calculate the flux of the vector field through the given surface.  F = 2i −3j + 6x2yk through the…

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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: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x³i + yj+ z°k out…

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Q: Calculate the net outward flux of the vector field F = xy i + (sin xz + y2)j + (exy2 + x)k over the…

A: Given surface 'S' is surrounding region D bounded by the planes y=0, z=0, z=2-y and z=1-x2

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: 4. Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = v3;1 v3;173…

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Q: Evaluate the surface integral Js F · dS for the given vector field F(x,y, z) = 7xi+ 4yj+7zk and the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the net outward flux of F =axr across any smooth closed surface in R, where a is a constant…

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Q: The outward flux of the vector field F(x, y, z) = (x, y, z?) across the boundary of D = {(x, y, z) E…

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Q: Let Q be the solid region bounded by the surface S of equation given by z2 = x2 + y2 , 0 ≤ z ≤ 3,…

A: Find outward flux of the vector field G(x, y, z) = x2 i+ y2 j+ z2 k with Q the solid region bounded…

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

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Q: Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across ơ, where o is the portion of the…

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Q: Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = x³i + y³j+z³k…

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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: 2u?u? Σ: y = u with 0<u < 2,0 < v< 1. Z = V

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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: Let S be the part of the plane 2x + 5y + z = 4 which lies in the first octant, oriented upward. Find…

A: Given, S be the part of the plane                        2x+5y+z=4        which lies in the first…

Q: Find the flux of the force field F(x, y, 2) = (2, x + r², 1 – a² + y) across the portion of the…

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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: find the outward flux of F across the boundary of D. F = xz i + yz j + k D: The entire surface of…

A: Consider the given vector field. F = xz i + yz j + k

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: 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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Q: Use the Divergence Theorem to find the outward flux of the vector field F(x, y, z) = x³i + y³j+ z³k…

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