Let S be the part of the plane 4x + 3y + z = 4 which lies in the first octant, oriented upward. Use the Stokes theorem to find the flux of the vector field F = 2i +2j + 2k across the surface S.

Q: Let S be the part of the plane 3r + ly +z = 3 which lies in the first octant, oriented upward. Use…

A: given plane 3x+y+z=3 which lies in the first octant oriented upward.  use stokes theorem to find the…

Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

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Q: .3 Evaluate || F · dS, where F = and S is the helicoid with vector equation r(u, v) = 0<u < 1, 0 <…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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

A: To find the flux of the vector field F across the surface S. F=x2yi−zk S is the portion of the cone…

Q: Determine the flow of the vector field (image 1), through the surface S, outwards, with S being the…

A: Given :- The flow of the vector field through the surface S , outwards , with S  being the…

Q: 2. Let C be the curve of intersection between the cylinder r2+y = 1 and r-2y+z = 0, oriented…

A: The complete solutions are given below

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

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Q: Calculate the flux of the vector field F = (yz, xy, 3) through the elliptical cone S given by the…

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Q: a are calculating the yield percent for lettuce. You determine that the yield is 103% You are How do…

A: It is found that the yield percent for a lettuce is 103%. The yield percent of an object gives the…

Q: Let S be the part of the plane 2x + 4y + z = 4 which lies in the first octant, oriented upward. Find…

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Q: Compute the flux of the vector fields F(x,y, z) = (, y, z) across the 1 and z = 4 whose vertical…

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Q: Use Stokes' Theorem to find the work done by the force field F= on a particle that traverses counter…

A: Given data: The force field is F→=z3,12x,y The equation of circle is C:x2+y2=9 in the plane z=5.

Q: Let F = –9zi+ (xe*z – 2xe*² ) }+ 12 k. Find f, F •dÃ, and let S be the portion of the plane 2x + 3z…

A: Given, F→=-9zi^+xexz-2xex2j^+12k^ and S be the portion of the plane 2x+3z=6 0≤y≤4

Q: a) Compute the flux of the vector field F = (-2, 3, z³) across the disk in the xy- plane of radius…

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Q: Let S be the part of the plane 3r+ ly +z = 3 which lies in the first octant, oriented upward. Use…

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Q: Find the outward flux of the field F = 8xyi + 4yzj + 2xzk across the surface of the cube cut from…

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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.