Math 220 Class Slides
http://math.albany.edu/pers/hammond/course/mat220/
February 14, 2008
1.
No class Tuesday the 19th
University in Recess
2.
Assignment due February 21
Expect a
quiz
.
Read Matthews, §§ 8.5 – 8.7
Exercises:
Matthews,
186:
8 – 12
3.
Exercise No. 1
Where does the line
L
through
A
=
3
,
−
2
,
7
and
B
=
13
,
3
,
−
8
meet the plane
z
=
0
? The general point on
L
is
φ
t
=
A
+
t
B
−
A
=
1
−
t
A
+
t
B
=
3
+
10
t
,
−
2
+
5
t
,
7
−
15
t
as
t
varies in
R
. It crosses the plane
z
=
0
when
15
t
=
7
, i.e., at the point
φ
7
⁄
15
=
23
3
1
3
0
.
4.
Exercise No. 4
A
=
2
,
3
,
−
1
B
=
3
,
7
,
4
Want
P
on
A
B
so that
P
A
⁄
P
B
=
2
⁄
5
If
P
=
1
−
t
A
+
t
B
, then
P
A
A
B
=
t
P
B
A
B
=
1
−
t
P
A
P
B
=
t
1
−
t
Determine
t
such that
t
1
−
t
=
2
5
or
t
1
−
t
=
±
2
5
Hence,
t
=
2
⁄
7
or
t
=
−
2
⁄
3
.
P
1
=
5
⁄
7
2
,
3
,
−
1
+
2
⁄
7
3
,
7
,
4
=
16
⁄
7
,
29
⁄
7
,
3
⁄
7
or
P
2
=
5
⁄
3
2
,
3
,
−
1
−
2
⁄
3
3
,
7
,
4
=
4
⁄
3
,
1
⁄
3
,
−
13
⁄
3
5.
Exercise No. 5
A
=
1
,
2
,
3
B
=
−
2
,
2
,
0
C
=
4
,
−
1
,
7
M
is the line through
A
parallel to
B
C
M
:
φ
t
=
1
,
2
,
3
+
t
6
,
−
3
,
7
=
1
+
6
t
,
2
−
3
t
,
3
+
7
t
E
=
1
,
−
1
,
8
F
=
10
,
−
1
,
11
N
is the line through
E
F
N
:
ψ
u
=
1
−
u
1
,
−
1
,
8
+
u
10
,
−
1
,
11
=
1
+
9
u
,
−
1
,
8
+
3
u
The intersection:
φ
t
=
ψ
u
one vector equation
=
3 scalar equations in
t
and
u
6.
Exercise No. 5: Solving the Equations
1
+
6
t
=
1
+
9
u
2
−
3
t
=
−
1
3
+
7
t
=
8
+
3
u
6
t
−
9
u
=
0
−
3
t
=
−
3
7
t
−
3
u
=
5
t
=
1
and
u
=
2
3
Point of intersection:
φ
1
=
ψ
2
⁄
3
=
7
,
−
1
,
10