Figure 5.4 illustrates the vector difference
between
and
. From the coordinates, we compute
.

Figure 5.4:
Geometric interpretation of a
difference vector.

Note that the difference vector
may be drawn from the tip of
to the
tip of
rather than from the origin to the point ; this is a
customary practice which emphasizes relationships among vectors, but the
translation in the plot has no effect on the mathematical definition or
properties of the vector. Subtraction, however, is not commutative.

To ascertain the proper orientation of the difference vector
,
rewrite its definition as
, and then it is clear that the vector
should be the sum of vectors
and
, hence the arrowhead is on the
correct endpoint. Or remember `` points to ,'' or `` is from
.''