circ semicolon equals ModifyingAbove phi With ampersand c period circ semicolon"/>
In a spherical coordinate system, unit vectors are defined as
(1.9)
which leads to
(1.10b)
(1.10b)
(1.10c)
1.2.1.2 Vector Operations and Properties
Dot Product
The dot product between two vectors results in a scalar quantity. One simple application example for a dot product is the work that is done by a force for displacement from one point to another. Consider vectors
(1.11)
If θ between two vectors is 90°, then the dot product of these two vectors is equal to zero.
Figure 1.2 (a) Representation of vectors
Figure 1.3 Unit vector representation in a Cartesian coordinate system.
Cross Product
The cross product between two vectors is also a vector. The magnitude of the cross product of
(1.12)
(1.13)
Vector Operation Properties for Dot and Cross Products
Some of the properties for dot and cross products are given below
(1.14a)
(1.14b)
(1.15a)
(1.15b)
(1.16a)
