24/01/2022 6 The flux of the curl of the vector field F(x, y, z) = (y², x, 2) through the surface Σ= {(x, y, z) = R³ z = y + 5, x² + y² ≤ 1}, oriented in such a way that its normal vector ñ satisfies the condition n k > 0, equals A π (B) -π (C) 0 (D) π/2 Stokes theorem & carl f π do = fF Tds

24/01/2022 6 The flux of the curl of the vector field F(x, y, z) = (y², x, 2) through the surface Σ= {(x, y, z) = R³ z = y + 5, x² + y² ≤ 1}, oriented in such a way that its normal vector ñ satisfies the condition n k > 0, equals A π (B) -π (C) 0 (D) π/2 Stokes theorem & carl f π do = fF Tds

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 13P

See similar textbooks

Similar questions

2. For the vector field F (x, y, z) = (x²y, xyz, −x²y²) F(x, y, z)=(x2y,xyz,-x2 y 2 ), find: (a) div (F)div (F) (b) curl (F)curl(F) (c) div (curl (F))
Let F(x, y) = ⟨xy^2+2x+1, x^2y − 3y⟩ be a vector field. Let C be the curve thatconsists of two line segments C1 and C2, where C1 has vertices (−1, 0) and (0, 1)and C2 has vertices (0, 1) and (1, 0). C is oriented clockwise.(a) Sketch C accurately.(b) Find the work done by F by moving a particle along the path C in the givendirection.
f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?
Sketch the vector field F(x,y)=1/2xi-1/2yj at points (-1,1), (-1,0),(-1,1),(0,-1),(0,0),(0,1),(1,-1),(1,0),(1,1)
Compute the flux of the vector field = yi + 53 − xzk through the surface S, which is the surface y = x² + z², with x² + z² ≤ 1, oriented in the positive y-direction. flux =
Sketch and describe the vector field F (x, y) = (-y,2x)
For the vector field (x³z², 0, -x²z), evaluate the line integral on the clase curve made by a square in the (x, 2) plane with corners at (1,0,1), (-1,01), (-1,0, -1), (1, 0,-1) in the counter clockwise direction.
Find the curl of the vector field F. F(x, y, x) = 2yz'i + 3xj +&xk O 1534 O 15z3 O (8yz3 – 8]j + (6xy- 24)k O 8yz + 6xy3-24-8
a) Show that F (x, y) = (yexy + cos(x + y)) i + (xexy + cos(x + y) j is the gradient of some function f. Find f b) Evaluate the line integral ʃC F dr where the vector field is given by F (x, y) = (yexy + cos(x + y)) i + (xexy + cos(x + y) j and C is the curve on the circle x 2 + y 2 = 9 from (3, 0) to (0, 3) in a counterclockwise direction.
We are given a vector field and a parametric curve
Find the flux of the vector fieldF(x, y, z) =(x)i+(y)j+(z)kthrough the surface S of the paraboloid z=x^2 + y^2, for 0 ≤ z ≤ 9,where the unit normal n to S has a negative k component. (This the flux through the side of the paraboloid.)
Find the curl of the vector field F = < yx³, xz³, zy² curl F = انم I'S 18 j + k - +