calculate the flux of the rotational field from G`(x, y, z) = yi→ + x² j→ + zk→ r`(u, v) = (u, v, 2u + v + 1) NY through u ≥ 0, v ≥ 0, u + v ≤ 2 with normal pointing down and to

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 curl(curlF→(x,y,z)) of the vector field F→(x,y,z)=x^9zi→−9x^8zj→+yzk→. Enter the exact answer.…

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Q: Suppose the vector field v(x, y, z) = (−y − 2) i + (4z − 2) j + (z − 1) k represents the velocity…

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Q: Let F = (x^2 + y^2, x^2 + y^2) be a vector field and C be the simple closed curve given by circles…

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Q: Find the value of the line integral ∫CF→⋅dr→if F→(x,y)=(y^3+11)i→+(3xy+11)j→is a conservative vector…

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Q: Show that F : R^2 → R^2,F(x,y) = (x + y^2,2xy + 2y^2) is a gradient vector field, and find the…

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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)…

A: Using divergence theorem calculate the flux:  φ=∯SF.dS   =∰V∇.F.dv…

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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: 8xz Calculate line integral F. dr of conservative vector field F(x, y, z) = i Y A from (-4, 2, 1) to…

A: we have to find the line integral  ∫AF.dr where F(x,y,z)=8xzyi-4x2zy2j+4x2yk and A is path from…

Q: 1) F(x, y, 2) = 3xyi + 2yz j+ 7xz k. 3) F(x, y, z) = 6 e" senyi + 2e* cos yj + 9z k. 5) F(x, y, z) =…

A: We will find out the required value .

Q: Find the total flux of the vector field F= (x^2 z)i + (y^2 z)j+(z^3)k through the closed surface of…

A: Given vector field is  F=x2zi+y2zj+z3k              (i) Given surface is  x2+y2=16z=2z=-2 Let us…

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Q: Compute the flux of the vector fields F(x,y, z) = (, y, z) across the 1 and z = 4 whose vertical…

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Q: Let ryz , (교2 + y"), 17 F = ( x2 +y? be a vector field on U = {(x, y, z) E R³ | (x, y) # (0, 0)}.…

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Q: Let C' be the straight line curve between the points (0,7) and (1,0). Let N be the unit normal…

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Q: Compute the flux of the vector field ♬ = zi +67 through the parameterized surface S' oriented upward…

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Q: Find the work done when a particle moves in the force field 3x² i + (2xz-y)j + zk a) The straight…

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Q: 6. (a) Determine whether the given velocity vector of a fluid is rotational or irrotational. I) F(x,…

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Q: Verify Green’s Theorem for the vector field F(x, y) = (x^2*y^2 , xy) and the closed curve C…

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Q: 5) Find the work done by the force field F =-yzi+xz j +xy k as the point of application moves from…

A: Yes, the amount of work done in this case is independent of the path taken. This is because the…

Q: In a vector field V = (y^a,−x^b,z^c) what is the value of the z-component of curl (V) at (x, y, z) =…

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