Читать книгу RF/Microwave Engineering and Applications in Energy Systems - Abdullah Eroglu - Страница 23

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).

(1.28)

The magnitude of vector is found from

(1.29)

The vector can be illustrated in the spherical coordinate system, as shown in Figure 1.8.

In Figure 1.8, the range of R, θ, and ϕ are given as

Figure 1.7 Representation of vector in a spherical coordinate system.

Figure 1.8 Representation of vector in a spherical coordinate system.

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

(1.30)

(1.31)

The base vector properties are then equal to

(1.32)