RF/Microwave Engineering and Applications in Energy Systems. Abdullah Eroglu
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(1.6c)
In a cylindrical coordinate system, unit vectors are defined as
(1.7)
Hence
(1.8a)
(1.8b)
(1.8c)
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)