Give a formula F = M(x, y)i + N(x, y)j for the vector field in the plane that has the properties that F = 0 at (0, 0) and that at any other point (a, b), F is tangent to the circle x + y = a² + b? and points in the clockwise direction with magnitude |F| Va? + B.

Q: Please compute the work done by the vector field F(r, y) = (sin r+ry?)i+(ev+ a)j in R?, where C is…

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Q: Find an equation of the plane through the origin such that the circulation of the field F = zi + xj…

A: Given the circulation of the field F = zi + xj + yk along the intersection of the planeand the…

Q: Sketch the vector field in the plane along with its horizontal and vertical components at a…

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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: Use the Divergence Theorem to calculate the flux of the vector fields F, = -2zi + 2xk and F2 = -2zi…

A: DIVERGENCE THEOREM I=∫∫∫div V dV=∫∫∫ ∇.V dV=∫∫V∫∂∂x+∂∂y+∂∂zdV GEOMETRICAL INTERPRETATION OF…

Q: 5) By using Stokes' Theorem, find the work performed by the vector field Ex² + 4xy³i+ y²xk,on a…

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Q: xi + yj x2 + y2 F(x, y) = k-

A: Topic- vector integration

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

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Q: Use the Divergence Theorem to calculate the flux of the vector fields F1 = -8zi + 8ak and F2 = -8zi…

A: Given vector fields are F1→=−8zi^+8xk^ and F2→=−8zi^+y+2j^+8xk^ We have to calculate the flux of the…

Q: Find the flux of the vector field F(x, y, z) = ri across the outward oriented sphere %3D

A: In this question, we find the flux of the vector field f(x,y,z)=xi The surface is a sphere of radius…

Q: Let F = (0, x), a 2D vector field. Compute fF . T ds, where C is the top half of the circle of…

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Q: Find the curl of the vector field F(x, y, z)= e sin yi - e cos yj.

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Q: Find the divergence of the vector field F. F(x, y, z) = In(9x2+ 6y² )i + 54xyj + In (6y? + 5z?)«…

A: To find the divergence of given vector field

Q: For the vector field F(x, y, z) = (15x2y + 2xz)i + (5x3 + 35y4)j + x2k, show that F is conservative…

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Q: Find the work done by the vector field F= in moving an object along C in the positive direction,…

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Q: Find the work done by the vector field F = (– 4z, – 3y, – 2x) in moving an object along C in the…

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Q: 3) Given the vector field F = circulation around the triangle formed by the intersection of the…

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Q: for the vector field F = 2xz i+ (1 – 4xy² ) j led by the plane z = 6 – 2x² – 2y² and the plane

A: We have to find the following conditions according to the given information

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, a) + (2y-3')] + 7k…

A: Solution :

Q: Find the work done by the vector field F = ( – 2, – 4y, 2æ) in moving an object along C in the…

A: Let F be a vector field defined on a smooth curve C whose parametric equation is given by rt, a≤t≤b.…

Q: Q1 Use Stokes theorem to compute the flux of the curl of a vector field F = (2x – y)ĩ – yz? j- y²zk…

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Q: Calculate the flux of the vector field through the given surface.  F = 2i −3j + 6x2yk through the…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F =x3y 2i+yj…

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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: Please compute the work done by the vector field F(x, y) = (sin x+xy²)i+(e" + a2)j in R?, where C is…

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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: find the work done by the given vector field F along the specified curve C.   F(x, y) = yi − x j,…

A: Given, F(x,y)=yi^-xj^ where curve, x2+y2=4 W=∫F.dr W=∫ydx-xdy from curve, dx=-dy W=∫xdx+ydy limit of…

Q: Calculate the line integral , F · dr, where C is the straight-line path from (2,0) to (0,2),…

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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: . Verify that Stokes' theorem is true for the vector field F(r, y, z) = (x, y, 2), where S is the…

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Q: disk

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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: 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: Find g(x, z) so that F(x, y,z) = (8x cos y sin? z + 2e2xz)î – (4x² sin y sin? z)j+ (g(x, z) cos y +…

A: Given that    Fx,y,z=8x cosy sin2z+2e2xz i^-4x2 siny sin2z j^+gx,zcosy+2e2xz k^ Now we have to find…

Q: Find the work done by the vector field F = (- 3z, 4y, 2x) in moving an object along C in the…

A: Work done by any vector field F is given by ∫F.dr where r is the position vector. Dot product is the…

Q: Find the flux of the constant vector field i = -4 i – 5j- 2 k through a square plate of area 16 in…

A: The solution is given below

Q: Give a formula F = M(x, y)i + N(x, y)j for the vector field in the plane that has the properties…

A: Given information:

Q: Find the surface integral to evaluate the flux of the vector field F=, where S is the surface of the…

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Q: Use Stoke's Theorem to find the work done by the force field F(x, y, 2) = (ein + 2y?, 6x + tan- y,…

A: Given : force field              F→x, y, z=esinx+2y2, 6x+tan-1y, xz To find : work done by the force…

Q: Calculate the line integral , F · dr, where C is the straight-line path from (2,0) to (0,2),…

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

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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: Find the outward flux of the vector field i- .+72 across the surface of the region that is enclosed…

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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: Use Green Theorem to find the work done by the force field, F(x, y) = (e* + x²y,e – 2xy) in moving a…

A: According to Green's Theorem  ∫CPdx+Qdy=∬D(∂Q∂x−∂P∂y)dA where F→ = ⟨P, Q⟩

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: Let C be the helix that winds around the cylinder x2+y? = 1 (counterclockwise viewed from the…

A: here i used parametric equation of helix and done simple calculation like dot product and after that…

Q: Find the divergence of the vector field F. F(x, y, 2) = In(7x2+ 6y? )i + 42xyj + In(6y2. + 72² )«…

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Q: Sketch the vector field F(x, y) = 3i + 5j and calculate the flux then the circulation of F| along…

A: (1) The equation of line segment is: x+3-2+3=y-1-5-1=tx+3=t⇒x=t-3y-1=-6t⇒y=-6t+1 The curve…