Biomedical Engineering Reference
In-Depth Information
z
F
θ z
4ft
θ y
y
θ x
2ft
6ft
x
FIGURE 4.3 Three-dimensional vector defined by its magnitude and line of action.
The quantity in parentheses is the unit vector of F ,or
!
2 i
4 k
2 2
þ
6 j
þ
p
e F ¼
¼
0
:
267 i
þ
0
:
802 j
þ
0
:
534 k
6 2
4 2
þ
þ
and the magnitude of F is
p
2
67 2
02 2
34 2
j F
:
þ
8
:
þ
5
:
¼
10 lb
The vector F in Figure 4.3 may also be defined in 3-D space in terms of the angles between
its line of action and each coordinate axis. Consider the angles y x
, y y
, and y z
that are
measured from the positive
x
,
y
, and
z
axes, respectively, to F . Then
cos y x ¼ F x
j F j
ð
4
:
5
Þ
cos y y ¼ F y
j F j
ð
4
:
6
Þ
cos y z ¼ F z
j F j
ð
4
:
7
Þ
These ratios are termed the
direction cosines
of F . The unit vector e F is equivalent to
e F ¼
cos y x
i
þ
cos y y
j
þ
cos y z
k
ð
4
:
8
Þ
or, in general
0
@
1
A
F x
i
k
F
þ F y
j
þ F z
e F
¼
q
ð
4
:
9
Þ
2
2
2
z
x þ F
y þ F
Search WWH ::




Custom Search