Evaluate the surface integral ∫∫S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y i + (z-y) j + x k S is the surface of the tetrahedron with vertices (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1).

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

A:

Q: Compute the flux of the vector field F = 4yỉ + 4j − 4xzk through the surface S, which is the surface…

A:

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

A:

Q: Consider two vector fields in the xy plane, given in the Cartesian coordinates as: U(x, y) = 4c(y +…

A:

Q: A vector field is specified as G = 24xyax + 12(x² + 2)ay + 18z²az. Given two points, P(1, 2, - 1)…

A: Given: G=24xyax+12x2+2ay+18z2az P1,2,-1 Q-2,1,3 To find: c Unit vector directed from Q to P. d…

Q: Find the flux of the vector field F = across the part of the plane 3+x+2y above the rectangle [0,…

A:

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

A:

Q: Let F(x, y) = (4x², 3y2). Compute the flux F nds of F across the boundary of the triangle with…

A:

Q: Parametrize this surface. Calculate the flux of the vector field F(x,y,z)=(xy,xz,zx) through the…

A: As per the question we are given the following surface : S : z = x sin(y) , 0≤x≤2 , 0≤y≤π And the…

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

A:

Q: ) For the scalar potential function = (x² + y² + z²)² and the velocity vector field u-(y², z, x²)…

A: Answer

Q: Please don't provide handwritten solution .....

A: To find the exact answer, let's first compute the double integral over the region ( R ) defined by…

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

A: