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MATH 203 Final Exam, December 2011
Instructions:
Complete every question in Part I (Questions 17.) Complete three of
the ﬁve questions in Part II (Questions 812). Each question is worth 10 points.
No calculators or other electronic devices may be used during the examination. Answers
may be left in terms of
√
7
,
sin(3)
,π
, etc. if needed. Give reasons for all answers. This
exam will last 2 hours and 15 minutes. Good luck!
1. (a) Find an equation for the plane through the points
A
= (0
,
1
,
2),
B
= (1
,
0
,

1),
and
C
= (1
,
2
,
3).
(b) Find parametric equations for the line through (4
,
1
,
3) and perpendicular to
the plane found in (a) above.
(c) Let
~v
=
h
0
,
2
,

2
i
Is the line found in (b) perpendicular to
~v
, parallel to
~v
or
neither of these?
2. At points (
x,y,z
) in a region of space for which
x
2
+
y
2
≥
1 and
z
≥
0, there is an
electric charge
E
(
x,y,z
) =
z
+
z
ln(
x
2
+
y
2
).
(a) Find the rate at which the electric charge is changing at (1
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 Spring '11
 snell
 Math

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