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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).

(1.23)

The magnitude of vector is found from

(1.24)

The vector can be illustrated in the cylindrical coordinate system, as shown in Figure 1.6.

In Figure 1.6, the range of r, ϕ, and z are given as

The vector operations for dot and cross products for vectors and are given by

(1.25)

(1.26)

Figure 1.6 Representation of vector in a cylindrical coordinate system.

The base vector properties can be obtained as

(1.27)