The outward flux of F(x, y, z) = xi + yj + zk across any unit cube is.

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

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Q: Let F(x, y) = 3 i + j + 2k, and let S be a square whose side lengths are 3, parallel to the…

A: Flux is F.dA Where F is the Field and A is the area

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: Find the flux of F(x,y,z) = sin(xyz) i+ xy j + ze*/5 k across the part of the cylinder y? + 2 z? = 4…

A: According to question,Fx,y,z= sin xyzi +xy j + z ex5 k,equation of cylinder,y2 + 2z2 =4planes, x = 1…

Q: Let F(x,y,z) = ztan(y2) i + z³In(x² + 4)j+z k. Find the flux of F across the part of the paraboloid…

A: Given that, F(x,y,z)=ztan-1(y2)i+z3ln(x2+4)+zk To find flux of F: Divergence theorem:…

Q: Compute (i * j) * j and i * (j * j). What can you conclude about the associativity of the cross…

A: Note that :

Q: 2. The task is to determine the flux of B across G, where G is the positively-oriented portion of…

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Q: Compute the flux of the vector field F(x, y, z) = 2xj+ 4yk through the surface S, where S is the…

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Q: Use the divergence theorem to find the flux of F = [x²yz, -xy² z, 6 – 5z2| on the hemisphere S =…

A: Consider the given function. The divergence theorem is defined as. Now, find the value of div F.

Q: Use the divergence theorem to calculate the flux of F = (x - 8y)i + (y – 4z)j + (z - 8x)k out of the…

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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…

Q: Use the Divergence Theorem to find the flux of F(x, y, z)=z³ i-x³j+y³ k across the sphere x² + y² +…

A: This is a problem of vector calculus.

Q: Let S be the cylinder x2 + y2 = a2, 0<=z <=h, together with its top, x2 + y2 <=a2, z = h.…

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Q: Determine the work done by the force field F(x, y, z) = (x − y2, y −z2 , z − x2) on a particle that…

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Q: Find the net outward flux of F = a x r across any smoothclosed surface in ℝ3, where a is a constant…

A: Net outward flux is ∇.F ∇=i∂∂x+j∂∂y+k∂∂za=a1i+a2j+a3kr=xi+yj+zk

Q: Compute the flux of F = (5(z + 2), 5, 52) through the surface S given by y = ² + 2, with 0 0, z 2 0,…

A: We have to find flux.

Q: Find the work done by the force field F(x, y, z) = (x - y2, y – z2, z - x2) on a particle that moves…

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Q: Find the work done by the force field F(x, y, z) = (y + z, x + z, x + y) on a particle that moves…

A: It is known that

Q: Find the flux of the vector field F(x, y, z) = (yz, y°, xz) %3D across the surface S, where S is the…

A: Given

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: 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: Let F(x, y, z) = z tan-¹(y²)i + z³ In(x² + 3)j + zk. Find the flux of F across S, the part of the…

A: The given problem is to find the flux of vector field over the given surface of part of the…

Q: Compute the flux of F= xi+yj+ z*k across the cone z =Vx2 + y? , 0szs1, in the downward direction.…

A: We have to find the flux in the downward direction.   Let us assume that x=rcosθ, y=rsinθ, z=r Then…

Q: Find the work done by the force field F(x, y, z) = (x − y², y - z², z - x²) on a particle that moves…

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Q: Use the Divergence Theorem to find the flux of F(x, y, z) = 3x°i+ 3.x²yj+ 33xyk across the surface…

A: According to the given information, it is required to use the divergence theorem to find the flux.

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: Find the flux of F across S, where F(x,y,z) = xˆi + yˆj + zˆk and S is the part of the cone z = √x2+…

A: Surface integral problem

Q: Compute the flux of F(r, y, z) = [1,–2, z] through the surface S, which is part of the graph z =…

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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: Use the divergence theorem to calculate the flux of F = (x - 9y)i + (y – 5z)j + (z – 3x)k out of the…

A: The divergence theorem mathematically states that:

Q: Let  F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 10)j + zk.  Find the flux of F across S, the part of…

A: let, F(x,y,z)=ztan−1(y2)i+z3ln(x2+10)j+zk Find the flux of F across the part of the…

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

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Q: Find the outward flux of the field F = 3xz2 i + y j - z3 k across the surface of the solid in the…

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Q: Evaluate F-N dS and find the outward flux of F(z,y, z) = ryî+yzj-yzk, through %3D the surface S of…

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Q: Let F(x, y, z) = z tan−1(y2) i + z3 ln(x2 + 8) j + z k. Find the flux of F across S, the part of the…

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Q: 7. Find the flux of F(z,y, 2) = ri+yj+zk through the portion of the paraboloid z = 1+z²+y° that is…

A: Given

Q: oriented

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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: Let - (xz, 5 - 4xyz, xz) be the velocity field of a fluid. Compute the flux of i across the surface…

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Q: 5. If F = (x,2y,3z), the outward flux of F across the boundary of a unit cube (volume equal to 1) is…

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Q: Let F(x, y) = (2x + y³, 2y – x4). Compute the flux oF. F.n ds of F across the circle of radius 5…

A: Given function can be written as, Region bounded by the circle of equation,

Q: Find the flux of F(x,y,z) = (-x,-y, z³) , across S. Where S is the part of the cone z = /x² + y²…

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Q: Let S be the cylinder x² + y² =a²2, 0≤zsh, together with its top, x² + y² sa², z = h. Let F = -7yi +…

A: Given : Surface S is the cylinder x2+y2=a2, 0≤z≤h, together with its top, x2+y2≤a2, z=h and  F→=-7y…

Q: Find the flux of the force field F(x, y, 2) = (2, x + r², 1 – a² + y) across the portion of the…

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Q: find the outward flux of F across the boundary of D. F = xz i + yz j + k D: The entire surface of…

A: Consider the given vector field. F = xz i + yz j + k

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: Find the flux of the vector field (y, x, z) in the negative z direction through the part of the…

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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: Find the work done by the force field F(x, y, z) = (x – y², y – z², z – x2) on a particle that moves…

A: We have to find the work done by the force field F(x,y,z)=&lt;x-y2, y-z2, z-x2&gt; on a particle…