Calculate the flux of the vector field of (xv.z = r-)i +0= 4xz) i +xzk across the box bounded by *=y =Z= 0,x = 2,y = 2,2 = 3. O A 36

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: 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 V(x, y, z) = 3xy²i + 5x²yj + 2z³k out of the unit sphere. Flux =

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Q: Compute the work done by the vector field F(x, y, z) = (,2, 2yz) when moving a particle: 1+? > a)…

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Q: 5) By using Stokes' Theorem, find the work performed by the vector field Ex² + 4xy³i+ y²xk,on a…

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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: Compute the flux of the vector field F 3.ri + 3yj through the cylindrice surface shown below, if a=3…

A: To calculate the flux of the vector field.

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

A: To find the curl for the vector field  at the given point.Fx, y, z=6xyzi+6yj+6zkPoint=6, 7, 6

Q: 4. Is the vector field F(r, y, :) = (yz,rz, ry) conservative? Justify your answer.

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Q: Calculate the flux of the vector field F(x, y, z) = 5i + 2j+ zk through the closed circular cylinder…

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Q: Let divF(x,y, z) = 4x³ + 4y³ + 42³ , where F represents the flow of a vector field. Estimate the…

A: Concept Used:- Divergence Theorem Flux=∫∫∫∇.F dVwhere ∇.F is the divergence of FVolume of the…

Q: Compute the flux, || Foñds, across the slanted face of the tetrahedron 2 = 4-1- y bounded in the…

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Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

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Q: From the given vector field F⃗ (x, y, z) = , compute the curl of F⃗ and find the values of a and b…

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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: Compute the flux of the integral of the vector field F(z,y, 2) = (2,y, 2) through the half cylinder…

A: Given vector field is, Fx,y,z=x,y,z. It can be written as,  Fx,y,z=xi^+yj^+zk^. Flux of 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: 2. Show that V(V × F) = 0, here vector field is twice differentiable. %3D

A: This question is from vectors.

Q: Compute the flux of the vector field (x, - xy*), out of the rectangle with vertices (0,0), (5,0),…

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Q: Determine if the vector field F=(yz,xz,xy) is conservative?

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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 = 2xi + 5yj through the cylindrical surface shown below, if a…

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Q: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 5 for fluid flowing…

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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: Verify the Divergence Theorem in the calculation of the flux of the vector field: through the…

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Q: Compute the flux of the vector field F = 3xzi + 5yk through the surface S, which is the hemisphere…

A: The flux is given byflux =∫S  F→·n^  dShere,n^=x, y, zx2+y2+z2 in spherical coordinatesF→·n^ =x, y,…

Q: Compute the flux of the vector field (x2, - xy*), out of the rectangle with vertices (0,0), (4,0),…

A: Given,

Q: Compute the flux of the vector field (x, (æ°, – ay*), out of the rectangle with vertices (0,0),…

A: To compute the flux of the vector field x3,-xy4, out of the rectanglewith vertices 0,0,2,0,2,4…

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: Compute the flux of the vector field F = across sphere a? + y² + z² = 9.

A: Let F be a vector field and S be the boundary of the surface D. To find the flux of the vector…

Q: Verify that the vector field f is conservative and find its scalar potential. 3r f = + yz + 2xz) i+…

A: If the vector field f:ℝ3→ℝ3 is continuously differentiable in a simply connected domain  and curl…

Q: Determine if the vector field is conservative. 1 -) (yi + «j) F(x,y) = 1+ xy, conservative not…

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Q: Calculate the work done in moving a particle in the force field F = 3x2î+ (2xz-y)ĵ+ z k along a…

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Q: Let divF(x, y, z) = 4x³ + 4y3 +4z³, where F represents the flow of a vector field. Estimate the flux…

A: Given divF→x,y,z=4x3+4y3+4z3radius r=0.1 Centered at point 1,1,1

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

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Q: Calculate the line integral of the vector field F = -3 i+ 2j along the line from the point (4, 0) to…

A: To find the line vector of following vector fieldF→=-3i+2jalong the line 4,0 and 12, 0

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

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Q: Find the curl of the vector field F=(2xyz, -xy,-z^2)

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Q: Calculate the line integral of the vector field F = -2i+ 4jalong the line from the point (3,0) to…

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Q: 3. Find a potential for the conservative vector field: F(x, y, z) = (2xy + 2x, x² – 2yz³, -6z –…

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Q: Compute the flux of the vector field (x3, – xy³), - out of the rectangle with vertices (0,0), (3,0),…

A: Given: F=x3 ,-xy5with rectangle with vertices (0,0) , (3,0) , (3 ,2) , (0,2) To find flux of vector…

Q: Show that the vector field F(x, y, 2) = (2x cos y – 3)i – (x² sin y + 2²)j – (2yz – 2)kis a…

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Q: Calculate the flux of the vector field F 6i + 2x2j- 2k, through the square of side 4 in the plane y…

A: Given vector field is F→=6i→+2x2j→−2k→ We have to find the flux of the given vector field. The flux…

Q: The outward flux of the vector field F=(x,0, z) across the cylinder x + y = 1, for 0<z<1, is %3D…

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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…

A: Given the vector field F=z-2x,y+2z,-2y+x around the triangle with vertices 0,0,2,2,0,0 and 0,2,0.…

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 flux of the constant vector field i= -4 i-5j-2 k through a square plate of area 16 in the…

A: The objective is to find the flux.

Q: Find the flux of the vector field J = 2x?yi + 4zj ou t of the closed box 0 < x < 2,0 < y< 8,0 < z <…

A: We have to find the flux

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.