Q2) Find the flux of the vector field F(x,y,z) = (x,y, z) , where the surface S is the portion of the paraboloid z = 1- x² – y? and xy - plane. (downward orientation)

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: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…

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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 a potential for the conservative vector field: F(x, y, z) = (2xy + 2x, x² – 2yz³, –6z – 32²y²)…

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Q: Use the Divergence Theorem to compute the flux across the sphere x2+y2+z2 = 1 within the vector…

A: The answer is as follows:

Q: Compute the flux of the vector field F(x, Y, z) = 6i + 5j + 3k through the rectangular region with…

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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: 3. Use the Divergence Theorem to find the flux of the vector field F = (5x+ 4y?z – 162³) i +…

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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 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: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 3| for fluid flowing…

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Q: I. Use the Divergence Theorem: (² F. ds = Ifv. Fav SSS E = to calculate the flux of the field F…

A: Divergence theorem uses  Double integration converts into triple integration.

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z)=-3ry-ly:j-Szak…

A: To find- Use the divergence theorem to calculate the flux of the vector field F→x, y, z = -3xyi^ -…

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

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Q: 4. The vector field F(x, y) = (x² – y²)i+ 10-Rj-2zrk represents the velocity of a gas flowing in…

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

A: Given :-  The flux of the vector field  F→ =  x3 , z , -y through the helicoid with the…

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: Use the divergence theorem to calculate the flux of the vector field F(x, y, a) + (2y-3')] + 7k…

A: Solution :

Q: Calculate the outward flux of the vector field F→ (x,y,z) = 2xi→ + yi→ +zk→ along the boundary of…

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Q: Calculate the outward flux of the vector field F→ (x,y,z) = 2xi→ + yi→ +zk→ along the boundary of…

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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: Evaluate the outward flux of the vector field F = (2x² – 5e" + sin(z²), –4ry + In(x*), 5z – 3x²y®)…

A: We can see that the region given here is closed, so…

Q: Q1 Use Stokes theorem to compute the flux of the curl of a vector field F = (2x – y)ĩ – yz? j- y²zk…

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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: 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 upward flux of the vector field F(x,y,z)= (-y, x, 9) across the part of the hemisphere…

A: Consider the provided question,

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: Find the curl and the divergence of the vector field. F(x, y, z) = x²yzi - x³y k i + Submit Answer…

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

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Q: . Verify Stoke's theorem for the vector field F = (2x - y) I– yz²J -y z K over the upper half…

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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 flux of the vector field F = across the part of the plane | z = 2 + x + 3y above the…

A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…

Q: Use the extended divergence theorem to compute the total flux of the vector field F(x, y, 2) 3D…

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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: Let F be the vector field (x², 2r, 2²). Let C be the boundary of Lv **---- the surface S given by…

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

A: Given that a small sphere of radius 0.1, centered at the point  (1, 1, 1).And                  div F…

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: Find the flux of the curl of the vector field F(x, y, z) = [(z2 −4) cos(xyz), 3x+y,(z2 −4) sin(ex…

A: Surface is oriented outwards. And -2 &lt;= z &lt;= 2

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: 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: A hot air balloon is shaped like a truncated sphere like the figure. The gases escape through the…

A: Given a hot air balloon has a truncated spherical shape. The velocity vector field  Vx,y,z=∇×Fx,y,z…

Q: Compute the flux of the vector field F = 2xzi + 5yk through the surface S, which is the hemisphere…

A: In this question, we find the flux for the given vector field across the surface of the hemisphere.

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 F = [x,y,z] through the oriented surface S: z= x^2 + y^2, z <= 1…

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Q: Determine whether the vector field…

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Q: Find the flux of the vector field F(x, y, z) = [x4, −4yx3, 7z + sin(xey))] through the outwards…

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