2. Let F(x, y) -yi-zj + zk be a vector field. Compute F FdS, where S is the hemisphere a² + y² +₂² 1, ≥ 0, oriented in the direction of the positive z-axis. =

Q: What is the flux through the described surface?

A: The surface is described by The vector field is F=<1, 3x, 2y>To evaluate the Flux for the…

Q: ector product of two vector fields: V × (F x G) = (V · G)F – (V · F)G + (G · V)F – (F · V)G %3D

A: Part iii Given, The identity of the vector product of two vector fields is proved.

Q: Let F(z, y) be the vector field plotted below, and let C be the piecewise-linear path from (8, –5)…

A: Draw the linear path from 8,-5 to 8,5 to 10,5, which is given below.

Q: Find the k-component of (curl F) for the following vector field on the plane. F = (Xex)i + (8y ex)j…

A:

Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

A:

Q: Consider the square C oriented counter clockwise, with vertices (0, 0), (2, 0), (0, 2), (2, 2) and 7…

A:

Q: Determine whether the line integral of each vector field (in blue) along the semicircular, oriented…

A: Determine whether the line integral of each vector field along the semicircular or oriented path is…

Q: A4. Which of the following vector fields is not the curl of another vector field? A. F=zi+=j+yk B.…

A:

Q: This is a two part problem. A. Compute the curl of the vector field F = (7yz, 5xz, 3xy). B. What is…

A:

Q: F(x, y) = -¹ + (y-x)j 1 1 -11 1-1 1 T 1 71 1-1 1 I 1 1

A: The given vector field is F=-18i+y-xj. To Sketch: Vector field F.