Graphics Reference
In-Depth Information
where is any scalar quantity. Therefore, we must get used to statements such as
p
=
2
r
−
3
s
These scalar multipliers provide a useful problem-solving strategy, as we shall see in later
chapters.
When we add scalar quantities, we know that their sequence has no effect on the final result.
For example, 2
+
6
=
8 and 6
+
2
=
8. Fortunately, this is the same for vectors. For instance, if
r
=
s
+
t
, then we can also state that
r
=
t
+
s
. This is shown graphically in Fig. 1.9(a), which
illustrates the meaning of
r
=
s
+
t
. But equally, we can reverse the vector sequence to create
=
+
r
t
s
, as shown in Fig. 1.9(b).
t
s
r
s
r
t
(b)
(a)
Figure 1.9.
When we subtract scalar quantities, their sequence is important. For example, 2
−
6
=−
4, but
6
4. However, if we consider adding positive and negative scalar quantities together, we
find that 2
−
2
=+
4. This, too, has a vector equivalent, and it is worth
investigating how this combination is represented graphically.
The operation
r
+
−
6
=−
4 and
−
6
+
2
=−
=
s
+
t
is shown in Fig. 1.9(a), but to draw
r
=
s
−
t
, it is best to consider it
as
r
=
s
+
−
t
, as shown in Fig. 1.10. The process involves drawing the vector
t
, reversing it to
create
−
t
, and adding
s
to
−
t
.
−
t
t
s
r
=
s
-
t
s
+
t
Figure 1.10.
1.3 Non-collinear vectors
When two vectors are
collinear
, we imply that the vectors possess the same orientation but
could have different lengths. It means that one vector must be a scalar multiple of the other.
If two vectors are
non-collinear
, then it is impossible for one to be a scalar multiple of the
