EXAM 1
MATH 22
Name:
____________________________
Winter 2001
Section: __________
You have
50 minutes
to complete this test. You must
show all work
to receive full credit.
1. Given
,
and
.
Find the following:
a
→
=< 
11
2
, ,
b
→
=< 
01
1
, ,
c
→
=< 
110
, ,
(a)
,
(b) The angle between
and
.
a
b
→
→
+
a
→
b
→
(c) A
unit vector that is orthogonal to both
and
.
b
→
c
→
2. Determine whether the lines
and
are parallel, skew or intersecting. If they
intersect find the point of
L
1
L
2
intersection.
:
,
,
,
:
,
,
.
L
1
x
t
= 
6
y
t
= +
1
9
z
t
= 
3
L
2
x
s
= +
1
2
y
s
= 
4
3
z
s
=
3. Given the points
,
,
and
.
P
( , , )
012
Q
( , , )
2 4 5
R
(
, , )

101
S
( ,
, )
6
14

(a)
Find the volume of the parallelepiped determined by the vectors
,
and
.
PQ
→
PR
→
PS
→
(b)
Are the three vectors
,
and
coplanar? Explain.
PQ
→
PR
→
PS
→
4. (a)
Find an equation of the plane through the point
and perpendicular to the line
,
(
, ,
)

2 8 10
x
t
= +
1
,
.
y
t
=
2
z
t
= 
4
3
(b) Find the distance from the point
to the plane
.
( ,
, )
0
10

x
y
z
  =
2
2
1
5. Find the traces of the surface given by
in the planes