Biomedical Engineering Reference
In-Depth Information
(f) Consider the vector
b
=
2
e
x
+
3
e
y
+
e
z
. Determine the column rep-
b
according to the bases
resentation of
{
e
x
,
e
y
,
e
z
}
,
{
a
x
,
a
y
,
a
z
}
and
{
α
x
,
α
y
,
α
z
}
.
a
y
·
b
a
y
×
b
a
y
·
b
(g)
Show that:
a
x
×
=
a
x
·
=
×
a
x
.
1.6
Assume
{
e
x
,
e
y
,
e
z
}
is an orthonormal vector basis. The following vectors
are defined:
a
=
4
e
x
+
3
e
y
−
e
z
b
=
e
y
−
e
z
6
e
x
−
e
z
.
Are
a
,
b
and
c
linearly independent? If not, what is the relationship between
the vectors?
c
=
8
1.7
The vector bases
{
e
x
,
e
y
,
e
z
}
and
{
x
,
y
,
z
}
are orthonormal and do not
coincide:
(a) What is the effect of
e
x
x
+
e
y
y
+
e
z
z
acting on a vector
a
?
(b) What is the effect of
x
e
x
+
y
e
y
+
z
e
z
acting on a vector
a
?
The vector basis
{
e
x
,
e
y
,
e
z
}
is orthonormal. What is the effect of the
following dyadic products if they are applied to a vector
1.8
a
?
(a)
e
x
e
x
.
(b)
e
x
e
x
+
e
y
e
y
.
(c)
e
x
e
x
+
e
y
e
y
+
e
z
e
z
.
(d)
e
x
e
y
−
e
y
e
x
+
e
z
e
z
.
(e)
e
x
e
x
−
e
y
e
y
+
e
z
e
z
.
