Biomedical Engineering Reference
In-Depth Information
i j k
A
x
A
y
A
z
B
x
B
y
B
z
¼
A
B
i j k
321
ð
4
:
14
Þ
¼
2310
¼
i
½ð
2
Þð
10
Þð
1
Þð
3
Þ
j
½ð
3
Þð
10
Þð
1
Þð
2
Þ þ
k
½ð
3
Þð
3
Þð
2
Þð
2
Þ
¼
i
ð
20
3
Þ
j
ð
30
þ
2
Þþ
k
ð
9
þ
4
Þ
¼
17
i
32
j
þ
13
k
lb ft
EXAMPLE PROBLEM 4.1
The vector
F
in Figure 4.5 has a magnitude of 10 kN and points along the dashed line as shown.
(a) Write
F
as a vector. (b) What is the component of
F
in the
x
-
z
plane? (c) What moment does
F
generate about the origin (0,0,0)?
y
F
15m
x
9m
12m
z
FIGURE 4.5
Force vector
F
has magnitude of 10 kN.
Solution
This example problem is solved using MATLAB. The
prompt denotes input, and the percent
sign, %, precedes comments ignored by MATLAB. Lines that begin without the
>>
prompt are
MATLAB output. Some spaces in the following output were omitted to conserve space.
>>
>>
%(a) First write the direction vector d that points along F
>>
% as a 1D array:
>>
d
¼
[12 -15 9]
¼
d
12 -15 9
>>
% Now write the unit vector of F, giving its direction:
>>
¼
unit_vector
d/norm(d)
¼
unit_vector
0.5657 -0.7071 0.4243
