Exam 1 will be given on Thursday, Sept 30th, covering sections 12.1–12.5, 13.113.4. No make
up exam will be given unless you have an absolutely valid excuse. In the exam, show all your
work and explain what you are doing. Answers will be graded on the accuracy and clarity of
the work shown.
1. Review the relevant homework assignments.
2. Review all examples given in my lectures.
3. Let
~a
= (6
,
2
,
3),
~
b
= (

1
,
5
,
2) and
~
c
= (1
,
0
,
1).
Find (1)
~a
+ 3
~
b

2
~
c
;
(2)
~a
·
~
b
;
(3)
~a
×
~
b
;
(4)

~
c

;
(5) Proj
~
c
~
b
;
(6) the area of the
parallelogram determined by
~a
and
~
b
.
(7) the volume of the parallelepiped determined
by
~a
,
~
b
and
~
c
.
4. Find a parametric equation for the line through the points (3
,
1
,

1) and (3
,
2
,

6).
5. Find an equation for the plane through the points (3
,
1
,

1), (3
,
2
,

6) and (1
,
1
,
0).
6. Find an equation for the plane that passes the point (1
,
1
,

1) and perpendicular to the
line
x
= 2
t
+ 1
,y
= 3
t

2
,z
=

4
t
+ 1.
7. Find an equation for the plane consisting all points that are equidistant from the points
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This note was uploaded on 10/07/2010 for the course MTH 555555 taught by Professor Xingruzhang during the Fall '10 term at SUNY Buffalo.
 Fall '10
 XingruZhang

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