Compute the flux of the vector field F = <xy, 5yz, 6zx> through the portion of...

Compute the flux of the vector field F = <xy, 5yz, 6zx> through the portion of the plane 3x + 2y + z = 6 in the first octant with the downward orientation.

Expert Solution

milcah answered 2 years ago

Let F be a vector field. Find the flux of F through the given surface. Assume...

Let F be a vector field. Find the flux of F through the given surface. Assume the surface S is oriented upward. F = eyi + exj + 24yk; S that portion of the plane x + y + z = 6 in the first octant.

Use the extended divergence theorem to compute the total flux of the vector field F(x, y,...

Use the extended divergence theorem to compute the total flux of the vector field F(x, y, z) = −3x2 + 3xz − y, 2y3 − 6y, 9x2 + 4z2 − 3x outward from the region F that lies inside the sphere x2 + y2 + z2 = 25 and outside the solid cylinder x2 + y2 = 4 with top at z = 1 and bottom at z = −1.

Calculate the flux of the vector field F? (r? )=9r? , where r? =?x,y,z?, through a...

Calculate the flux of the vector field F? (r? )=9r? , where r? =?x,y,z?, through a sphere of radius 4 centered at the origin, oriented outward. Flux =

Find the flux of the vector field F = x i + e2x j + z ...

Find the flux of the vector field F = x i + e2x j + z k through the surface S given by that portion of the plane 2x + y + 8z = 7 in the first octant, oriented upward.

Find the flux of the vector field F = (3x + 1, 2xe^z , 3y^2 z...

Find the flux of the vector field F = (3x + 1, 2xe^z , 3y^2 z + z^3 ) across the outward oriented faces of a cube without the front face at x = 2 and with vertices at (0,0,0), (2,0,0), (0,2,0) and (0,0,2).

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )over the path C consisting of line segments joining (1,1,1) to (1,1,2), (1, 1, 2) to (1, 3, 2), and (1, 3, 2) to (4, 3, 2) in 3 different ways, along the given path, along the line from (1,1,1) to (4,3,2), and finally by finding an anti-derivative, f, for F.

Use the divergence theorem to calculate the flux of the vector field F⃗ (x,y,z)=−5xyi⃗ +2yzj⃗ +4xzk⃗ through...

Use the divergence theorem to calculate the flux of the vector field F⃗ (x,y,z)=−5xyi⃗ +2yzj⃗ +4xzk⃗ through the sphere S of radius 2 centered at the origin and oriented outward. ∬SF⃗ ⋅dA⃗ =

(8pts)Consider the following vector field F and closed oriented curve C in the plane a. compute...

(8pts)Consider the following vector field F and closed oriented curve C in the plane a. compute the circulation and interpret the result b. compute the flux of the vector field F across C F = <y,-2x>/sqrt(4x^2+y^2) r(t) = <2cost,4sint>

Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along...

Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along the curve which is given by the intersection of the cylinder x 2 + y 2 = 4 and the plane x + y + z = 2 starting from the point (2, 0, 0) and ending at the point (0, 2, 0) with the counterclockwise orientation.

Find the flux of the vector field V(x, y, z) = 7xy2i + 2x2yj + z3k...

Find the flux of the vector field V(x, y, z) = 7xy2i + 2x2yj + z3k out of the unit sphere.

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