APMA 212
Fall 2006
Final Exam
Section
:____
Name
: ______________________________________
Directions:
This test is ten pages long, not including the cover sheet.
There are 24 problems.
Space on these pages should be adequate for your work—if not, use the last page of this test.
Multiplechoice problems will be graded allornothing.
Work carefully and circle the correct answer.
On other problems, record your final answer in the answer box provided.
NOTE
: If you are asked to use a specific theorem in solving a problem, you must use the specified theorem
in order to obtain credit for your work!
Show your work on all problems (even multiplechoice) to obtain credit
.
No Notes
No Books
No Calculators
Good Luck!!!!!
Write and sign the pledge
Page
Weight
Score
1
10
2
10
3
12
4
14
5
8
6
10
7
12
8
8
9
8
10
8
TOTAL
100
Thursday, December 7, 2006
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APMA212
Fall 2006
[2]
1.
Find radius of the sphere whose equation is
2
2
2
2
4
x
x
y
z
+
+
+
=
.
(A)
1
(B)
2
(C)
3
(D)
2
(E)
5
(F)
6
(G)
7
(H)
2
2
[2]
2.
Given the points
P(2, 5) and Q(3, 3), find the unit vector
in the direction of the directed line segment
PQ .
uuu
v
Answer:
[6] 3.
Let
be the line given by
2
,
1
,
and
1
2 .
intersects the plane
2
1
at the point P = (1, 2, 3).
Find the angle
makes with the plane.
L
x
t
y
t
z
t
L
x
y
z
L
=

=
+
=
+
+

=
.
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 Spring '08
 Mojaheri
 Vector Calculus, Stokes' theorem, 2 j, 3 k, 3 j

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