Biomedical Engineering Reference
In-Depth Information
F
P
e
Figure 2.1
The force vector
F
and unit vector
e
.
F
=
−|
F
|
e
2
F
=
|
F
|
e
1
e
1
e
2
Figure 2.2
Force vector
F
written with respect to
e
1
and written with respect to
e
2
.
|
F
|
e
denotes a unit vector
The magnitude of the force vector is denoted by
.If
the force vector may be written as
F
=
Fe
,
(2.1)
where
F
may be any rational number (i.e. negative, zero or positive). The absolute
value
|
F
|
of the number
F
is equal to the magnitude of force vector:
|
F
|=|
F
|
. (2.2)
In Fig.
2.2
the force vector
F
is written with respect to either the unit vector
e
1
or
with respect to the unit vector
e
2
that has the same working line in space as
e
1
but
the opposite direction. Since the unit vector
e
1
has the same direction as the force
vector
F
:
F
=|
F
|
e
1
.
(2.3)
e
2
has a direction that is opposed to
F
, therefore
F
In contrast, the unit vector
=−|
F
|
e
2
.
(2.4)
Example 2.1
Let the force vector
F
be given by
F
=
2
e
1
.
If the unit vectors
e
1
and
e
2
have opposite direction:
e
2
=−
e
1
,
then the force vector may also be written as
F
=−
2
e
2
.
