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then
2
3
2
3
2
3
2
3
1
2
3
4
5
6
1 + 4
2 + 5
3 + 6
5
7
9
4
5
4
5
4
5
4
5
a
+
b
=
+
=
=
,
2
3
2
3
2
3
2
4
−
−
−3
3
1
2
3
4
5
6
1 − 4
2 − 5
3 − 6
4
5
4
5
4
5
5
a
−
b
=
−
=
=
,
2
3
2
3
2
3
2
3
2
3
4
5
6
−3
0
1
2
3
4 + 7 − 1
5 + (−3) − 2
6 + 0 − 3
10
0
3
4
5
4
5
4
5
4
5
4
5
b
+
c
−
a
=
+
−
=
=
.
A vector cannot be added or subtracted with a scalar, or with a vector
of a different dimension. Also, just like addition and subtraction of scalars,
vector addition is commutative,
a
+
b
=
b
+
a
,
whereas vector subtraction is anticommutative,
a
−
b
= −(
b
−
a
).
2.7.2 Geometric Interpretation
We can add vectors
a
and
b
geometrically by positioning the vectors so
that the head of
a
touches the tail of
b
and then drawing a vector from
Figure 2.10
2D vector addition
and subtraction
using the triangle
rule.
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