Find the flux of the vector field F = 2r2i+ 2y²j+ 4k across o in the direction of positive orientation where o is the portion of the parapoloid %3D F(u, v) = u cos vi + u sin vj+ (1- u)k %3D with 1

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

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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: Express the vector field W = (x2 - y)a, + xza, in the (a) Cylinderical coordinate at P(p = 6, q =…

A: Cylindrical coordinates are ρ,ϕ,z now let us look at the general form of vector fieldW in…

Q: 2. Find the gradient of the following scalar functions: a) T = 8/(x+y+2:²) b) V=3x²y³z c) U =…

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Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: :::.. V : 5+j wi +4j Find the specific Scalar .(.. )

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

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Q: Compute the flux of the vector field F =2xi +3yj through the cylindrical surface shown below, if a=3…

A: Given that the vector field is F(x,y)=2xi+3yj Let us parametrize the cylinder as x=cosθ, y=sinθ, z=r…

Q: Find the gradient vector field of f(x, y, z) = x³y* + y° z³ + xz°.

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (1, 4)…

A: As per Bartleby guidelines I have authority to answer only one question. If you want other…

Q: Sketch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line…

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Q: Find the flux of the vector field F = xi + e6xj + zk through the surface S given by that portion of…

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Q: Find the work done by the vector field F = xi + 2xyj + 3xyzk on a particle that moves along

A: Introduction: The size of the region enclosed by the graph of the supplied function between two…

Q: = + 1³ 2³ +²²³ +22+ Calculate the flux of the given vector field F where S is the sphere centered at…

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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 flow of the vector field a = (x + 2y)i + (x + 2z)j − zk along the outer surface of the…

A: Given To find the flow of the vector field a→ = (x+2y)i→+ (x + 2z)j→ - zk→along the outer surface of…

Q: Let u = 2i - j, v = 4i + j, and w = i + 5j. Find specified scalar u . v + u . w.

A: We will apply dot product of vectors.

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

A: The solution is given below

Q: Calculate the divergence and the curl of this vector function.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4yk through the surface S, which is the hemisphere 2²-

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