APPM 2350 Summer 2006
Exam 1
June 21, 2006
1
INSTRUCTIONS:
Computers, calculators, books, notes, flying monkeys,
etc.
are not permitted.
Some (possibly) useful formulae are attached. Write your name, your instructor’s name, and the
color of your exam sheet on the front of your bluebook. Work all problems. Start each problem on
a
new page
. Show your work clearly and
box
your final answer. A correct answer with incorrect
or no supporting work may receive no credit, while an incorrect answer with relevant work may
receive partial credit.
1.
(a) Calculate the equation for the plane through the points
A
(
−
1
,
1
,
1)
, B
(1
,
−
1
,
1)
, C
(1
,
1
,
−
1).
(b) Calculate the distance between the point
P
(
−
1
,
−
1
,
0) and the plane from (a).
(c) Sketch and describe (in words) the curve of intersection between the plane
x
+
y
= 0
and the surface
x
2
+
y
2
−
z
= 1.
(d) Find a parametrization of the curve in (c).
2. Prove or disprove the following statements (be sure to state clearly whether you believe them
to be TRUE or FALSE):
(a) If
A
·
B
=
C
·
B
and
B
negationslash
=
0
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 Summer '07
 ADAMNORRIS
 Velocity, Osculating circle, surface x2, constant normal component

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