MAT397-2008Fall - MAT 397 FINAL EXAM Student ID NAME Circle...

MAT
397
FINAL
EXAM,
Decembcr 10,
2008
Student
ID: NAME:
Circle
your instructor's
name:
Bleier Coman
CraÌ-¡bc Kovalev Lu
Verchota
Write
your
answers
and
sìrow
all
youl wolk
on this
tcst.
Thele
are
9
problerns
on
9
pages
(including
this
covel sheet),
for
a
total of
100
points.
To
receive
full
or
partial
credit, the co¡¡ect rvorh leading
to
the
coÌr'ect
answel rnust be
wlitten down.
Ursu¡rpolted
arrswers
wiìl
roceive
little
ol
uo
credit.
Graphics
calculatols may bc
usccl.
Symboìic calculators, such
as
TI-89
or
TI-92,
may
not
be
used.
.t,ro
Iem
Score
1
10
,2
10
,
t)
10
4 10
5
15
6
10
7 10
B
15
9 10
Total
(
100
)

2
1.(10points)
Fir:icl
an
equation for the
plare cotrtairing the poiuts (1,
-4,
- 1), (2,
5,
4)
and
(-1,-7,-2)
2.(10
points)
Com¡ntc
the
angle between
the vectors
a:
(-3,
a)
and
b
-
(f
,2)

3,(10
points)
Given
lhe culve with vectoÌ
equation
r(¿)
:3sin¿i
+
3cos¿j
-l-
41.k,
fild
tho
following:
(a)
The
unit
tatrgerìt vectoÌ
lo tìle
curve
at thc point
where
/:
n.
(b)
Thc length of the
arc
oI the
curve where 0
(
ú
(
1

4
4.(10
points)