alt="ModifyingAbove upper A With right-arrow dot ModifyingAbove upper B With right-arrow equals upper A Subscript x Baseline upper B Subscript x Baseline plus upper A Subscript y Baseline upper B Subscript y Baseline plus upper A Subscript z Baseline upper B Subscript z"/>
(1.22)
1.2.2.2 Cylindrical Coordinate System
Unit vector representation for a cylindrical coordinate system is shown in Figure 1.5.
A vector representation for a Cartesian coordinate system is given by (1.23).
The magnitude of vector
(1.24)
The vector
In Figure 1.6, the range of r, ϕ, and z are given as
The vector operations for dot and cross products for vectors
(1.25)
(1.26)
Figure 1.6 Representation of vector
The base vector properties can be obtained as
(1.27)
1.2.2.3 Spherical Coordinate System
Unit vector representation for a spherical coordinate system is shown in Figure 1.7.
A vector representation for a Cartesian coordinate system is given by (1.28).
The magnitude of vector
(1.29)
The vector
In Figure 1.8, the range of R, θ, and ϕ are given as