A Classical Approach of Newtonian Mechanics

3 MOTION IN 3 DIMENSIONS 3.3 Vector displacement

R

O

Figure 11: A vector displacement

1.16 Vector displacement

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 displace-

ment 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 direc-

tion 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 r of some point R from the origin O can be visualized

as an arrow running from point O to point R. See Fig. 11. Note that in typeset

documents vector quantities are conventionally written in a bold-faced font (e.g.,

r) to distinguish them from scalar quantities. In free-hand notation, vectors are

usually under-lined (e.g., r).

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

r = (x, y, z). (3.1)

The above expression is interpreted as follows: in order to get from point O to

point R, first move x meters along the x-axis (perpendicular to both the y- and

z-axes), then move y meters along the y-axis (perpendicular to both the x- and

z

r

y

x