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152
CHAPTER 2. CURVES
θ
= 0
θ
= 2
π
Figure 2.21: Cycloid
pair
of equations. By contrast, the dynamic view of a curve as the path of
a moving point—especially when we use the language of vectors—extends
very naturally to curves in space. We shall adopt this latter approach to
specifying a curve in space.
The position vector of a point in space has three components, so the
(changing) position of a moving point is speci±ed by a function whose
values are vectors in
R
3
, which we denote by
−→
p
:
R
→
R
3
; this can be
regarded as a
triple
of functions:
x
=
x
(
t
)
y
=
y
(
t
)
z
=
z
(
t
)
or
−→
p
(
t
) = (
x
(
t
)
,y
(
t
)
,z
(
t
))
.
As before, it is important to distinguish the
vectorvalued function
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Equations, Vectors

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