Verify Stoke's theorem for the vector field F = (2x - y) I– yz"J - y z K over the upper half surface of x +y +z* = 1, bounded by its projection on the xy-plane.

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: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: Sketch the vector field F. F(x, y) = yi + xj √x² + y² 2

A: Given:The vector field  is given by .To Find:We have to sketch the given vector field.

Q: Find all points (a, b, c) on the sphere x2 + y2 + z2 = R2 where the vector field F = yz2i + xz2j +…

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Q: Find the flux of the vector field F = across the part of the plane z = 3 + 2x + 4y above the…

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Q: Consider the vector field F(x,y,z) = (3x²y)i + (x³ + 1) + (92²) and the curve C made up of the…

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Q: Compute the flux of the vector field F 3yi + 4j – 3xzk through the surface S, which is the surface y…

A: We apply formula for finding this

Q: Let F = be a vector field in space Find the potential function f(x,y,z) of F

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Q: Sketch the vector field of F = (-y,0) in the xy-plane. %3D

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Q: Compute the flux of the vector field - 5yi + 3j- 5azk through the surface S, which is the surface y…

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Q: Consider the function f(x, y, z) = x2 + (y+ 3)z + e-3x and the vector field- F = **'i- yzj – xk %3D…

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Q: Sketch the vector field F(x, y) = (-x − y, x - y) at the points (x, y) where x, y = {−1,0,1}.

A: Consider the given vector field, F→x,y=-x-y,x-y Here we need to sketch the vector field at the point…