Math E-21a – Fall 2009 – HW #3 problems
Problems to turn in on Thurs, Sept 24
:
Section 9.6
:
11. Sketch the graph of the function
(, ) 6 3 2
f xy
x
y
.
12. Sketch the graph of the function
(, ) c
o
s
x
.
34. Find an equation for the surface consisting of all points
P
for which the distance from
P
to the
x
-axis is
twice the distance from
P
to the
yz
-plane. Identify the surface.
Chapter 9 Review Exercises
:
8. Show that if
a
,
b
, and
c
are in
R
3
(also denoted
V
3
in the text) then
2
(
) [(
) (
)]
[ (
)]
ab bc ca
abc
.
10. Given the points
A
(1, 0, 1),
B
(2, 3, 0),
C
(–1, 1, 4), and
D
(0, 3, 2), find the volume of the parallelepiped with
adjacent edges
AB
,
AC
, and
AD
.
26. Find the distance from the origin to the line
1
,
2
,
1 2
x
ty
tz
t
.
36. Identify and sketch the graph of the surface
22
2
1
y
zx
. Include several traces (cross-sections) in your
sketch.
Section 10.1
:
In problems 6-8, sketch the curve with the given vector equation. Indicate with an arrow the direction in which
t
increases.
6.
32
()
,
tt
t
r
7.
,cos2,s
in2
t
t
r
8.