Math 20E, Practice Midterm 1
April 24, 2007
Name:
Section:
This exam consists of 7 pages including this front page.
Ground Rules
1. No calculator is allowed.
2. Show your work for every problem. A correct answer without any justification
will receive no credit.
3. You may use one 4-by-6 index card, both sides.
4. Show your ID on your desk.
Score
1
10
2
10
3
10
4
10
5
10
6
10
Total
60
1
This
preview
has intentionally blurred sections.
Sign up to view the full version.
1.
Let
a
= 2
i
+
k
and
b
=
-
i
+ 2
j
-
3
k
be vectors in
R
3
.
(a) Compute the orthogonal projection of
a
on
b
.
Answer
:
The orthogonal projection
p
is
p
=
b
·
a
||
b
||
2
b
=
-
2
-
3
1 + 4 + 9
b
=
-
5
14
b
=
5
14
i
-
5
7
j
+
15
14
k
.
(b) Compute
a
×
b
.
Answer
:
a
×
b
=
±
±
±
±
±
±
i
j
k
2
0
1
-
1 2
-
3
±
±
±
±
±
±
=
±
±
±
±
0
1
2
-
3
±
±
±
±
i
-
±
±
±
±
2
1
-
1
-
3
±
±
±
±
j
+
±
±
±
±
2
0
-
1 2
±
±
±
±
=
-
2
i
+ 5
j
+ 4
k
.
2
2.
(a) Let
f
:
R
3
→
R
given by
f
(
x, y, z
) =
x
2
+
y
2
+
z
2
-
2
z
. Describe level
surfaces by words.
Answer
:
f
(
x, y, z
) =
x
2
+
y
2
+
z
2
-
2
z
x
2
+
y
2
+ (
z
-
1)
2
-
1
.
For each
This
preview
has intentionally blurred sections.
Sign up to view the full version.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 04/30/2008 for the course MATH 20E taught by Professor Enright during the Spring '07 term at UCSD.
- Spring '07
- Enright
- Math, Vector Calculus
-
Click to edit the document details
