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.