Find the flux of the vector fielol F from the baunelries of the given region (o). 37 2. (D): solid sphere, x+4²ca²

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: Compute the flux of the vector field F = 5xi + 2yj through the cylindrical surface shown below, if a…

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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 tield F(x, y, z) = 67 + 27 + 4k through the rectangular region with…

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Q: Find the outward flux of the vector field F = (x³, y³, z²) across the surface of the region that is…

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Q: Compute the flux of the vector field F(x, y, z) = (2y, 3, –2xz) through the surface S, which is the…

A: Given vector field is, Fx,y,z=2y,3,-2xz. The given surface is, y=x2+z2  and  x2+z2≤1. Now for the…

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 of the vector field F = 5xi + 2yj through the cylindrical surface shown below, if…

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Q: ind the flux of the vector field F = yzi + 7yj + yk over the sphere x2 + y2 + z2 = 4.

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Q: A conservative vector field is given as F = 6xe'i + (3x²e' –10yz')j-15y 2 k. Find the potential…

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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 = (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…

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A: We have to find out conservative or not

Q: b) Find the flux of the vector field F(x,y,z) = 3xi – yj + 2zk; across o where o is the portion of…

A: The given question belonging to the vector calculus  in which we have to find the value flux of the…

Q: Compute the flux of the vector field F = 2xi + 5yj through the cylindrical surface shown below, if a…

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Q: Select the plot of the vector field F(z, y) = (2, z). %3D

A: Given vector field is F(x, y) = (2, x)

Q: 4. Find the flux of F = across the curved sides of the surface S = {(r, y, z)|z = cos y, |y| < T,0 <…

A: we have F→=e-y,2z,xy Surface S=x,y,zz=cosy,y≤π,0≤x≤4 Let z=gx,y=cosy ∂g∂x=0,∂g∂y=-sinyy≤π…

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: Calculate the flux of the vector field (x°, y), out of the annular region between the a + y? = 16…

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Q: Find the outward flux of the vector field F = (x°, y°, z²) across the surface of the region that is…

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Q: Determine whether the vector field is conservative. F(x, y) = 6y6(yi + 7xj) conservative not…

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Q: Find the divergence of the vector field. V(x, y, z) = 4yzi + 6xzj + xyk div(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: Determine if the vector field is conservative. 1 -) (yi + «j) F(x,y) = 1+ xy, conservative not…

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Q: Find the outward flux of F = (4x +25y*,0,) 10z through the surface 25 4 9

A: Solution:-

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: Compute the net outward flux across the sphere r²+y²+z (r*, y², 2ª).

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Q: F = 2xi+2yj+3zk and σ is the portion of the cone z=sqrt(x^2+y^2) between the planes z=3 and z=5…

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

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

Q: Find the net outward flux of F =axr across any smooth closed surface in R, where a is a constant…

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Q: Compute the flux of the vector field F = xi + yj + zk through the surface S, which is a closed…

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Q: Show that the following vector field is conservative and find the potential F(r, y, z) = (2ry, x² +…

A: The answer is given as follows.

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: ul for the through the box [o,8] x[ 0,41 x[0,2]. vector field f=<z,x, y2, calculate the rotalflux S.…

A: We need to calculate divergence . The formula for divergence for F=&lt;P,Q,R&gt; is ,…

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: Is the vector field F = [yze"yz, xze#yz, xye"yz] conservative? %3D O Yes O No

A: The vector field is conservative if ∇×F→=0 therefore, find ∇×F→ ∇×F→=ijk∂∂x∂∂y∂∂zyzexyzxzexyzxyexyz

Q: Find the divergence of the vector field. V(x, y, z) = 7e*Yj – 9e*Yj + 8EY²K - div(V) II

A: A detailed solution is given below.

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: 7. If it is the unit outward normal vector to any closed surface (S) bounding the region (V), pro…

A: 7 Given n→ is the unit out ward normal vector to any closed surface S bounding the region V. We have…

Q: he temperature in a temperature-controlled chamber is given by a 3D scalar field Tlx, y, 2) = Ax®yz…

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

Q: Select the irrotational vector field. OAyz 1-2xz1 + xyz k OB. yz 7 + xz 7 + xz R OCZ7 + z? Î + yz R…

A: We will find out the required value.

Q: 5) Integrate the vector field h a,y)= y2i+ (2xy-e*)J C parumetrizal by t€ £0, 5 3. over the circular…

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Q: Find the circulation and onotward flux of F = aroud and u2 %3D across the ellipee +- Circulation…

A: Given the vector field is F→=-y,x. Find the circulation and outward flux of F→ around and across the…

Q: Compute the outward flux of the vector field F = (5xy, 5y²) for the region enclosed by the curves y…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

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 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 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: Find the work done by the force field F(z,y,2) = Ir+v,rs, y+:) on a particle that moves along the…

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

A: We have to compute the flux of the  given vector field.

Q: Compute Sc F.d3 for the vedor field in the Cylinder with out ward facing and the surface which…

A: It is given that F→=xi+yj+ezk and the surface is x2+y2=4,1≤z≤5

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.