MATH 241, 1st Examination
Prof. Jonathan Rosenberg
Friday, September 30, 2005
Instructions.
Answer each question
on a
separate
answer sheet
. Show all your work.
Be sure your name, section
number, and problem number are on each answer sheet, and that you have copied and signed the honor pledge on the
first answer sheet.
The point value of each problem is indicated. The exam is worth a total of 100 points. In problems
with multiple parts, whether the parts are related or not, the parts are graded independently of one another. Be sure
to go on to subsequent parts even if there is some part you cannot do. Please leave answers such as
5
√
2
in terms of
radicals and
do not convert to decimals
.
You are allowed use of a nonprogrammable calculator and one sheet of notes.
1. (15 points, 5 per part)
Consider the lines
L
1
:
x

1
7
=
y

2
3
=
z,
L
2
:
x
+ 6
7
=
y
+ 1
3
=
z
+ 1
,
L
3
:
x

1

1
=
y

2
2
=
z,
L
4
:
x

1
=
y

2
2
=
z,
(a) Are
L
1
and
L
2
the same line? If not, are they parallel? If not, do they intersect? If they do intersect, do they
intersect perpendicularly? Explain.
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 Spring '08
 Wolfe
 Math, Calculus, @, Osculating circle, kappa, 2 %, MATLAB session, Prof. Jonathan Rosenberg

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