Game Development Reference
In-Depth Information
Figure 2.9
A 2D vector
multiplied by
various scalars
Some examples are
2
1
2
3
=
2
4
6
,
−3
−5.4
0
=
16.2
0
,
4.7
−6
8
/2 =
2.35
−3
4
.
Here are a few things to notice about multiplication of a vector by a
scalar:
•
When we multiply a vector and a scalar, we do not use any multi-
plication symbol. The multiplication is signified by placing the two
quantities side-by-side (usually with the vector on the right).
•
Scalar-times-vector multiplication and division both occur before any
addition and subtraction. For example 3
a
+
b
is the same as (3
a
)+
b
,
not 3(
a
+
b
).
•
A scalar may not be divided by a vector, and a vector may not be
divided by another vector.
•
Vector negation can be viewed as the special case of multiplying a
vector by the scalar −1.
2.6.2 Geometric Interpretation
Geometrically, multiplying a vector by a scalar k has the effect of scaling the
length by a factor of |k|. For example, to double the length of a vector we
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