Chapter 19 and 20 More Problems.
Consider the following:
G=x i+ y
j+(22 z)
k
=2 yz i+2 x xy+ z )
F
j+(
k
S1
is a portion of
S2
is the disk of radius 6 centered at (0,0,4), parallel to the xy-plane, oriented
z=10 x 2 + y 2
above the plane
z=4 , oriente
Math 223
Ch.19 Review
Name_
Calculate the flux of the vector field through the given surface.
1. F x 2 i y 2 j zk , and S is the cone z x 2 y 2 oriented upward with
x 2 y 2 1, x 0, y 0 .
2. F xze yz i xzj 5 x 2 y 2 k and S is the disk in xy-plane x 2 y 2
Review Ch.17
1. (a) Do lines x t , y 2 t , z 3 t and x 2 s, y 1 s, z s intersect?
When and where?
(b) Find the value(s) of c (if any) for which the lines l(t) = (c + 4t, 2 t, 3 + t)
and m(t) = (4t, 1 8t, 4 + 4t) intersect. When and where?
2. Write a param
Math 223
Ch.19 - 20
Extra Problems
1. Find the flux of F 2ei j through the given surface.
a. A square of side 3 perpendicular to the line x y , z 0 , centered at
1,1,0 and oriented away from the origin.
b. A disk of radius 3 in the plane x y 0 . The disk