Graphics Reference
In-Depth Information
The notation being developed here is very similar to that used in algebra. Indeed, vector
algebra is virtually identical to ordinary algebra, apart from a couple of things that we will
consider later on. For example, in algebra we can reason that if
x
=
2
+
b
and
b
=
c
+
d
then
x
=
2
+
c
+
d
Similarly, if
=−
x
6
then
−
x
=
6
We also know from algebra that if
x
=
10
+
b
then
10
=
x
−
b
So, can similar rules be used in vector algebra? Indeed, they can.
As we now know how to encode and interpret vector diagrams, let us see how we can identify
points along a vector. Consider, then, the vector
r
, as shown in Fig. 1.8. If vector
t
has an
identical orientation but is half the length of
r
, we can state
1
2
r
t
=
t
r
Figure 1.8.
But we could also reason that
r
=
2
t
, which is true and valid. And in general, we can state that
r
=
p
