Use the Divergence Theorem to find the flux of the vector field F = (3x2 – 3yz + 423) i + (4.xz – 2y2 + 8zx³) j + (4x³ – 5x³y² + 3z²) k through the surface S,oriented outward, consisting of x2 + y?,0 < z < 9, under the plane z = 9 and the part of the plane z = 9 inside the paraboloid. Check and clearly state if the conditions for Dvivergence Theorem are 4. the part of the paraboloid z = fullfilled. State what is W.

Q: Vz(x, y) V + y have the Show that all the vectors in vector field F same length, and state the…

A: The length or magnitude of a vector a, b is defined as follows: a, b=a2+b2 Note ca, b=ca, b, where c…

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: Find all points (a, b, c) on the sphere x2 + y2 + z2 = R2 where the vector field F = yz2i + xz2j +…

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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: Consider the vector field F(x,y,z) = (3x²y)i + (x³ + 1) + (92²) and the curve C made up of the…

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Q: 13. For the vector fields: A = x + 2y ŷ + 3z 2; B = 3y - 2x ŷ. Check both product rule given in…

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

A: Denote the unit sphere by S If the sphere is closed,  then the flux of v(x, y, z) out of S is given…

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: Compute the flux of the vector field F = ⟨xy, 3yz, 6zx⟩ through the portion of the plane 3x + 2y + z…

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Q: Find the curl of the vector field u = a) b) ▼xu =( V. (V x u) = = (7xyz², 6x² y³, 2x³ y³ z4 ).

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Q: Show that V² (v-x) = 2V.v+x-V²v, where v is a vector field and x is the position vector of a point…

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Q: Sketch the vector field of F = (-y,0) in the xy-plane. %3D

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Q: Calculate the curl of the vector = (2x + 3y)i + (y+z)j + (xy + 2zx)k

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj + yzk; (3,-9, 9) 15i…

A: To find the curl of the vector field at the given point.;

Q: Compute the flux of the vector field - 5yi + 3j- 5azk through the surface S, which is the surface y…

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