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Consider the motion of a body moving in 3 dimensions. The
body's instantaneous
position is most conveniently specified by giving its displacement from the origin of our
coordinate system. Note, however, that in 3 dimensions such a displacement possesses both
magnitude and direction. In other words, we not only have to
specify how far the body is situated from the origin, we also
have to specify in which direction it lies. A quantity which possesses both
magnitude and direction is termed a vector. By contrast, a quantity
which possesses only magnitude is termed a scalar. Mass and time are scalar
quantities. However, in general, displacement is a vector.
The vector displacement of some point from the origin
can be visualized as an arrow running from point to point . See Fig. 11.
Note that in typeset documents vector quantities are conventionally written in a boldfaced font
(e.g., ) to
distinguish them from scalar quantities. In freehand notation, vectors are usually
underlined (e.g., ).
Figure 11:
A vector displacement

The vector displacement can also be specified in terms of its coordinates:

(30) 
The above expression is interpreted as follows: in order to get from point to
point , first move meters along the axis (perpendicular to both the  and axes),
then move meters along the axis (perpendicular to both the  and axes),
finally move meters along the axis (perpendicular to both the  and axes).
Note that a positive value is interpreted as an instruction to move meters
along the axis in the direction of increasing , whereas
a negative value is interpreted as an
instruction to move meters
along the axis in the opposite direction, and so on.
Next: Vector addition
Up: Motion in 3 dimensions
Previous: Cartesian coordinates
Richard Fitzpatrick
20060202