Graphics Reference
In-Depth Information
α
X
F
2
=
4
F
1
+
F
2
α
F
1
=
6
Figure 2.10.
From Fig. 2.10, we find that
tan
−
1
−
4
6
3369
or 32631
=
=−
For the object to be in equilibrium the total force must be zero, which means that a third force
must be applied equal and opposite to
F
1
+
F
2
, i.e.,
−
F
1
+
F
2
=−
6
i
−
4
j
=−
6
i
+
4
j
Its direction is
tan
−
1
4
−
6
=
180
+
14631
=
2.8.2 Problem 2
Let's prove that the addition of two vectors is commutative, i.e.,
a
+
b
=
b
+
a
.
We begin by defining two vectors,
a
and
b
, as shown in Fig. 2.11.
C
b
B
a
a
+
b
A
Figure 2.11.
From Fig. 2.11, we get
=
−
AB and
=
−
BC
a
b
and
=
−
AB
+
−
BC
=
−
AC
a
+
b
(2.1)
But equally, we could have described the vector addition shown in Fig. 2.12.
