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 x y
x
y
.
12. Sketch the graph of the function
( ,
)
cos
f x y
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
(
) [(
)
(
)]
[
(
)]
a
b
b
c
c
a
a
b
c
.
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
t
y
t
z
t
.
36. Identify and sketch the graph of the surface
2
2
2
1
y
z
x
. 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.
3
2
( )
,
t
t
t
r
7.
( )
,cos2 ,sin 2
t
t
t
t
r
8.
( )
1
,3 ,
t
t
t
t
r
38. Two particles travel along the space curves
2
3
1
2
( )
,
,
( )
1
2 ,1
6 ,1
14
t
t t
t
t
t
t
t