Graphics Reference
In-Depth Information
C
b
B
a
a
b
+
a
D
b
A
Figure 2.12.
From Fig. 2.12, we have
=
−
AD and
a
=
−
DC
b
and
=
−
AD
+
−
DC
=
−
AC
b
+
a
(2.2)
From Eqs. (2.1) and (2.2), we have
a
+
b
=
b
+
a
2.8.3 Problem 3
+
+
=
+
+
Let us now prove that the addition of vectors is associative, i.e.,
a
c
.
Figure 2.13 shows four vectors forming a quadrilateral, where one diagonal is formed from
b
c
a
b
a
+
b
and the other diagonal is formed from
b
+
c
.
b
c
(b
+
c)
a
(a
+
b)
d
Figure 2.13.
It is obvious from Fig. 2.13 that
a
+
b
+
c
=
d
and
a
+
b
+
c
=
d
therefore,
a
+
b
+
c
=
a
+
b
+
c
