2. Use Gauss' Theorem to compute the outward flux of the vector field F(r) = (x, y, z²) through the solid tetrahedron bounded by the planes I = 0, y=0, z = 0, x+y + z = 1.

Q: Find the flux of the field F = 2xy i + 2yz j + 2xz k upward across the portion of the plane x + y +…

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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: 4. Find the positively oriented flux over the surface created by the paraboloid z = 16 – x² – y2…

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Q: 2. Verify that the vector field F(1, y, 2) = sec? y+ -32 2.r tan y + e csc r, 3e -32 cot x + sec z…

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Q: Compute the flux of the vector field F 3.ri + 3yj through the cylindrice surface shown below, if a=3…

A: To calculate the flux of the vector field.

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) = 6i + 5j + 3k through the rectangular region with…

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Q: Find a flux of the vector field ä(M)= (2z– y)i +6xj + yk through a part of the surface S: x - 4y+2z…

A: Given, a→M=2z-yi^ +6x j^ +y k^ Also given surface is, S: x-4y+2z-4=0 So the normal vector to the…

Q: Find the outward flux of the field F = (x + y)î + yĵ + zk across the closed surface: S: z = 16x² -…

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Q: (b) Compute the flux of the vector field F(x, y, z) = y i– 2.xyk over the triangle T with vertices…

A: Given vector field is: F→=yi^-2xyk^ Given vertices of the triangle are: 1,0,0, 0,1,0 and 0,0,2 Then…

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

A: Given that, The vector field F→x,y,z=5i→+5j→+6k→ through the rectangular region with corners at…

Q: Show that the vector field F = (x² cos y, e+y) is not a gradient vector field. %3D

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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: 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: 4. Compute the outward flux of the vector field F(r) = (r, y', =') through the unit sphere r² + y² +…

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

Q: Compute the net outward flux of the vector field F = (x i + y j + z k)/ (x2 + y2 + z2)^(3/2) across…

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Q: 2. Use Gauss' Theorem to compute the outward flux of the vector field F(r) = (x, y, z²) through the…

A: Outward flux by using gauss divergence theorem

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

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Q: Find the net outward flux of the fieldF = ⟨bz - cy, cx - az, ay - bx⟩ across any smooth closed…

A: The vector field is F=bz-cy,cx-az,ay-bx where a, b, and c are constants.

Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = Jx2 + y2 + 3 that…

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Q: Find the flux of the field F = x i + y j + z k across the sphere x2 + y2 + z2 = a2 in the direction…

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Q: Calculate the flux of the vector field (x, y³), out of the annular region between the x? + y? = 1…

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Q: Show that the vector field F(x, y, z) = (le* cos y + yz)i+(xz - e* sin y)j+(xy + 4z) k is a…

A: Given: F(x,y,z)= (excosy+yz)i+(xz-exsiny)j+(xy+4z)k To show that F is conservative and if it is,…

Q: (c) Determine the flux of the vector field F = x³i – 2yĵ + 7z²k across a cone z = x2 + y2 + 3 that…

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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: Compute the flux ∫F · n ds of F across the curve C for the given vector field and curve using the…

A: Solution; Consider the given function: F(x, y) = xy, x-y = P, Q P = x y Q = x -y and the boundaries…

Q: Why is the upward flux of a vertical vector field F = ⟨0, 0, 1⟩ across a surface equal to the area…

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

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Q: Calculate the flux of the vector field F = -2i + 5æ²j – 3k, through the square of side 2 in the…

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Q: Compute the flux of the vector field 1 F(x, y, z) = -k x² + y2 + 1 out of the conical container K =…

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Q: Find the flux in the upward z direction of the vector field F(x, y, z) = (xz³, yz³, (x² + y²)²)…

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Q: Find the flux of the field F up through the part of the 1+ xy paraboloid z = 1 – x² – y? that…

A: FORMULA: Flux=∬F.n^ dS According to Stokes theorem, ∬F.n^ dS =∬∇×F . n^ dS According to the…

Q: 4. (a) Show that the outward flux of the postion vector field F(x,y,z) = (x)7+ (y)] + (z) through a…

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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: Compute the flux of the vector field F = zi + 8xk through the parameterized surface S oriented…

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

A: Given F=xi+yj+zk ,-3<=x<=3,r=1

Q: Calculate the flux of the vector field F 6i + 2x2j- 2k, through the square of side 4 in the plane y…

A: Given vector field is F→=6i→+2x2j→−2k→ We have to find the flux of the given vector field. The flux…

Q: 2) Given that the total flux across the surface, S of the tetrahedron bounded by the planes x = 0, y…

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Q: 6) Given the vector field F = (-x,-y,-z) '(x²+y2+z²)3/2! write the integral to calculate the outward…

A: First we parameterize field F then we calculate the Flux across the sphere using following formula:

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: 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 <= z <= 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: Find the flux of the field F = z k across the portion of the sphere x2 + y2 + z2 = a2 in the first…

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Q: Compute the flux of the vector field F = 2xi + yj through the cylindrical 5 and b = 4 and it is…

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Q: Determine the flux of the vector field F = x³i – 2yĵ + 7z?k across a cone z = /x2 + y2 + 3 that lies…

A: Gauss theorem states that if V is a volume inclosed by a closed surface S then  flux=∫∫S F.n dS=∬∫V…

Q: Determine whether the vector field…

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Q: a) What is the flux of the constant vector field F = (a, b, c) through any closed surface? b) Is the…

A: Given That : A constant  vector field F=a,b,c and F=x3,y3,z3 To Find : i) The Flux through of…

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.