Vector Subtraction
Figure
5.4 illustrates the vector difference

between

and

. From the coordinates, we compute

.

Figure 5.4:
Geometric interpretation of a
difference vector.
![\includegraphics[scale=0.7]{eps/vecsub}](http://www.dsprelated.com/josimages_new/mdft/img704.png) |
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

.''
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