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1.2. VECTORS AND THEIR ARITHMETIC
21
prototype, we will consider
displacements
.
Suppose a rigid body is pushed (without being turned) so that a
distinguished spot on it is moved from position
P
to position
Q
(Figure
1.16
). We represent this motion by a directed line segment, or
arrow, going from
P
to
Q
and denoted
−−→
PQ
. Note that this arrow encodes
all the information about the motion of the
whole
body: that is, if we had
distinguished a di±erent spot on the body, initially located at
P
′
, then
its
motion would be described by an arrow
−−→
P
′
Q
′
parallel to
−−→
PQ
and of the
same length: in other words, the important characteristics of the
displacement are its
direction
and
magnitude
, but
not
the location in space
of its
initial
or
terminal points
(
i.e.
, its
tail
or
head
).
P
Q
Figure 1.16: Displacement
A second important property of displacement is the way di±erent
displacements combine. If we ²rst perform a displacement moving our
distinguished spot from
P
to
Q
(represented by the arrow
−−→
PQ
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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, Vectors

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