Graphics Reference
In-Depth Information
2.8 Position vectors
Imagine a point P in space with coordinates xyz. Obviously, there exists a vector whose tail
is at the origin and head is at P. Such a vector is called a
position vector
as it fixes the position
of P. What is useful, though, is that the vector's rectangular components are identical to the
Cartesian coordinates of the point, i.e.,
p
c
k
.
Before proceeding, let's take stock of what we have learned by applying this knowledge to
solve some simple problems.
=
x
i
+
b
j
+
2.8.1 Problem 1
An object is subjected to two forces F
1
and F
2
, where F
1
acts horizontally left to right, while
F
2
acts vertically downwards, as shown in Fig. 2.9. The problem is to find the magnitude and
direction of the resultant force and the force that would keep the object in equilibrium.
Y
F
2
= -4
j
F
1
= 6
i
j
i
X
Figure 2.9.
We begin by defining the forces as two vectors:
F
1
=
6
i
and
F
2
=−
4
j
Therefore, the resultant force is
F
1
+
F
2
=
6
i
−
4
j
The magnitude (length) is
√
6
2
√
52
F
1
+
F
2
=
+
4
2
=
=
7211
The direction of the force can be specified relative to the horizontal x-axis as shown in Fig. 2.10.
