Game Development Reference
In-Depth Information
2.5.1
Official Linear Algebra Rules
To negate a vector of any dimension, we simply negate each component of
the vector. Stated formally,
2
3
2
3
Negating a vector
a
1
a
2
.
a
n−1
a
n
−a
1
−a
2
.
−a
n−1
−a
n
4
5
=
4
5
.
−
Applying this to the specific cases of 2D, 3D, and 4D vectors, we have
Negating 2D, 3D, and
4D vectors
−
x y
=
−x
−y
,
−
x y z
=
−x
−y
−z
,
−
x y z w
=
−x
−y
−z
−w
.
Figure 2.8.
Examples of vectors and their negatives. Notice that a vector and its negative are
parallel and have the same magnitude, but point in opposite directions.
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