Name:
MTH 234 Section 60
Answers to Quiz 3, February 8 2011
The velocity vector of a curve is given by
v
(
t
) =
t
2
i
+ (2
t
+ 1)
j
+ (2
t
+
t
3
)
k
and the curve is at the point (1
,
0
,
1) when
t
= 0.
1. (2 points) Find the unit tangent vector to the curve when
t
= 1.
Answer:
T
(1) =
v
(1)

v
(1)

=
<
1
,
3
,
3
>
√
19
2. (2 points) Find the acceleration vector.
Answer:
a
(
t
) = 2
t
i
+ 2
j
+ (2 + 3
t
2
)
k
3. (3 points) Find the position vector of the curve when
t
= 1.
Answer:
r
(
t
) = (1
/
3)
t
3
i
+ (
t
2
+
t
)
j
+ (
t
2
+
t
4
/
4)
k
+
C
C
=
r
(0) =
i
+
k
r
(1) = (4
/
3)
i
+ 2
j
+ (9
/
4)
k
4. (3 points) Write an integral that gives the arc length of the curve from
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 Summer '10
 IrinaKadyrova
 Arc Length, Vector Space, Acceleration, Parametric equation, unit tangent vector

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