Find the flux of the vector field F across the surface S in the indicated direction. F =x3y 2i+yj -zk; S is the portion of the parabolic cylinder z = 1-y2 for which z 20 and 3sxs7; direction is outward (away from the x-y plane) 4 O-8

Q: Find the flux of the vector field F across the surface S in the indicated direction. F =x 4yi -z k;…

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

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Q: OSketch the vector field F(x, y) = -5i – 5j and calculate the line integral of F along the line…

A: Solution:-     Given that, F→ x,y=-5i∧-5j∧we have to calculate the line integral ∴we have to…

Q: Compute the flux of the vector field F = xi + 5yj through the cylindrical surface as shown in the…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F = 3x2j -z2 k;…

A: F = 3x2 j -z2 k,y = 2x2,0≤z≤2,-1≤x≤1.

Q: Consider the vector field Ĥ(x, y, z) = (y², x, z²). Let S3 be the portion of the paraboloid 2 = x² +…

A: Please comment if you need any clarification. if you find my answer useful please put thumbs up.…

Q: Find the curl of the vector field F. F(x, y, z) = (2y - z)i + e²j + xyzk

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Q: Find the flux of the vector field F k through the upper half of the sphere x + y + z² = 4. %3D pi…

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Q: (a) Calculate the work done in moving a particle in the vector field: F = xz i+ xy?j + 3xzk along…

A: Given that : F = xz i + xy² j + 3xz k along the intersection of the plane x + z = M and the cylinder…

Q: Find the flux of the vector field F across the surface S in the indicated direction. F = 6x i + 6y…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F= 6i+y4z8j-y…

A: According to the given information, it is required to find the flux of the vector field across the…

Q: Find the flux of the vector field F across the surface S in the indicated direction. F=x2y 5i+yj - z…

A: we have to find the flux of the vector field F=x2y5i+yj-zk across the surface S: portion of the…

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Q: Consider the vector field F = = (x + y)i+ (x² + y² )j. What is the downward flux across the line…

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Q: Consider again the vector field F = (x +y)i + (x² + y²)j_what is the downward flux across the line…

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Q: Consider the vector field given by F(x, y) = (6xy – 152 y)i + (3a? + 3y – 10a°y)j find a function…

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Q: Q2) Find the flux of the vector field F(x,y,z) = (x,y, z) , where the surface S is the portion of…

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

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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: Find the flux of the vector field F across the surface S in the indicated direction. F = 3x 2 j  -…

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Q: Find the outward flux of the vector field F (x, y, z) = x³i + y³j+(z³ + xz)k across the surface of…

A: The vector field given is as follows: Fx, y, z=x3i^+y3j^+z3+xzk^ We are asked to find the outward…

Q: Find the flux of the field F = x i + y j + z k outward through the portion of the cylinder x2 + y2 =…

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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: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…

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Q: The vector field F = (, i, 2²) has a scalar potential in the region R= {(x, y, 2) E R³ : r² + y? >…

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Q: X(t) 3t, 6. Determine whether the vector field is conservative and, if so, find a potential…

A: Given Fx ,y =6xy i + 3x2+6y2j

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Q: (b) Solve the electric flux through a paraboloid z = x? +y² – 16 that lies below plane %3D z= 0. It…

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Q: Find the flux of the vector field F = 2 i +3 j – 2 k through the rectangle with corners at (1,0,0),…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F = x 3y 2 i +…

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Q: Consider the vector field F (xr, y) = (2y - 12r*y", 4ry – 9r*y?) is conservative. (a) Show that F…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F = 8x i + 8y…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F = xi +yj+ z 2…

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Q: Find the path integral of a particle moving along a straightline connecting O(0,0,0) to A(1,1,1)…

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Q: F = 6x i  + 6y j + 7 k; S is "nose" of the paraboloid z = 2x 2 + 2y 2 cut by the plane z = 5;…

A: This is a problem of vector calculus.

Q: Find the divergence of the vector field F. F(x,y,2) %3D 6хe\i + 4ye'j

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

A: Find your answer below

Q: Determine whether the vector field is conservative, and, if so, find a potential function. (If the…

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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…

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Q: Let T(x, y,z) = x² + y² + z² represent temperature and let the 'flow' of the heat be given by the…

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Q: Evaluate the flux, in the specified direction, of the vector field across the surface. F(x, y, z) =…

A: To calculate the flux, we shall use the standard formula of flux in terms of the vector form of the…

Q: ind the flux of the vector field F across the surface S in the indicated direction. == x "yi -z k;…

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Q: A. Find the flux of a vector field = 8x i + 6y j+ 2z k through the portion of the plane z = 7 where…

A: As per the guidelines, I am supposed to do the first question only. Kindly repost the second…

Q: Find the flux of the vector field F(x, y, z) = 3i– 7 j+ zk where o is the portion of the cylinder x…

A: We need to find the flux of the given vector field F(x, y, z) = 3i - 7j + zk where σ is the portion…

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: Consider the vector field F (x+ y)i + (x² + y²)j What is the downward flux across the line segment…

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