Question

17

Find curl F

A) F=z^2xi+y^2zj-z^2yk

B) given vector field F= (x+xz^2)I +xyj +yzk, Find div and curl of F.

Answer #1

like please

Consider the vector field.
F(x, y, z) =
7ex sin(y), 7ey sin(z), 8ez sin(x)
(a) Find the curl of the vector field.
curl F =
(b) Find the divergence of the vector field.
div F =

Find the flux of the vector field F (x, y, z) =< y, x, e^xz
> outward from the z−axis and across the surface S, where S is
the portion of x^2 + y^2 = 9 with x ≥ 0, y ≥ 0 and −3 ≤ z ≤ 3.

Consider the vector field.
F(x, y,
z) =
6ex
sin(y),
7ey
sin(z),
5ez
sin(x)
(a) Find the curl of the vector field.
curl F =
(b) Find the divergence of the vector field.

Consider the vector field. F(x, y, z) = 9ex sin(y), 9ey sin(z),
2ez sin(x) (a) Find the curl of the vector field. curl F = (b) Find
the divergence of the vector field.

2. Is the vector field F = < z cos(y), −xz sin(y), x
cos(y)> conservative? Why or why not? If F is conservative, then
find its potential function.

(part a) Find the curl of F
F(x,y,z) = (x cos(y))i +
xy2j
(part b) Find the curl of F
F(x,y,z) = xyzi +
x2y2z2j +
y2z3k

Find the work done by the vector field F = 〈 2 xy + z/y , x^2 −
xz/ y^2 , x/y 〉 and C is the line segment that goes from (1,3,2) to
(1,4,6).

Consider the following vector field.
F(x, y, z) =
6yz ln x i + (3x −
7yz) j +
xy8z3 k
(a)
Find the curl of F evaluated at the point
(5, 1, 4).
(b)
Find the divergence of F evaluated at the
point (5, 1, 4).

Calculate the line integral of the vector field
?=〈?,?,?2+?2〉F=〈y,x,x2+y2〉 around the boundary curve, the curl of
the vector field, and the surface integral of the curl of the
vector field.
The surface S is the upper hemisphere
?2+?2+?2=36, ?≥0x2+y2+z2=36, z≥0
oriented with an upward‑pointing normal.
(Use symbolic notation and fractions where needed.)
∫?⋅??=∫CF⋅dr=
curl(?)=curl(F)=
∬curl(?)⋅??=∬Scurl(F)⋅dS=

Use the divergence theorem to calculate the flux of the vector
field F = (y +xz) i+ (y + yz) j - (2x + z^2) k upward through the
first octant part of the sphere x^2 + y^2 + z^2 = a^2.

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