Biology Reference
In-Depth Information
231
VECTORS
For two vectors in three dimension:
a
= a
x
i
+
a
y
j
+
a
z
k
,
and
b
=
b
x
i
+
b
y
j
+
b
z
k
,
where
i
,
j
and
k
are unit vectors along the x-, y- and z-axis. Their dot
product gives a scalar:
a
ยท
b
=
a
x
b
x
+
a
y
b
y
+
a
z
b
z
.
Their cross product is defined as:
= (
a
y
b
z
-
a
z
b
y
)
i
+ (
a
z
b
x
-
a
x
b
z
)
j
+ (
a
x
b
y
-
a
y
b
x
)
k
The direction of this vector is perpendicular to both
a
and
b
and follows the
right-hand rule.
The length of vector
a
equals to:
