Graphics Reference
In-Depth Information
n
a
b
sin θ
=
area = ab
sin θ
n
b
a
θ
Figure 2.22.
Before proceeding, it will be useful to prove that the above formulas are consistent, so let's
demonstrate that the rectangular unit vectors obey these rules.
Substituting i and j in Eq. (2.12), we get
i j k
100
010
i
×
j
=
00
10
01
00
10
01
i
×
j
=
i
+
j
+
k
=
k
Substituting j and k in Eq. (2.12), we get
i j k
010
001
j
×
k
=
10
01
00
10
01
00
j
×
k
=
i
+
j
+
k
=
i
Substituting k and i in Eq. (2.12), we get
i j k
001
100
k
×
i
=
01
00
10
01
00
10
k
×
i
=
i
+
j
+
k
=
j
both of which are correct. Now let's show how the vector product is sensitive to vector sequence
by reversing one of the above: substituting k and j in Eq. (2.12), we get
i j k
001
010
k
×
j
=
 
Search WWH ::




Custom Search