Coordinate system is used to represent any point, say P(x, y, z ) in space. There are many methods by which this can be done, but there are three simple methods, which we will discuss in this article.
Types of coordinate systems are :
I. Cartesian or rectangular coordinate system.
II Cylindrical coordinate system
III Spherical coordinate system.
Today I will discuss briefly about the cartesian or rectangular coordinate system:
Cartesian Coordinate System
In the cartesian coordinate system there are three coordinate axes mutually at right angles to each other and call them x, y, z axes. It is customary to choose a right handed coordinate system, in which the rotation from positive x axis towards the positive y axis is done (Try to make the figure). A point is located by x, y and z coordinates. These are the distances from the origin to the intersection of a perpendicular dropped from the point to the x, y and z axes respectively. Alternatively, the point may be considered as the intersection of the three surfaces, the planes x = constant, y = constant, and z = constant, the constants being the coordinate values of the point.
There are also unit vectors i, j, and k in x, y and z directions, respectively.
Properties of Unit Vectors :
Dot product of unit vectors:
cross product of unit vectors:
i x j = k
j x k=i
k x i =j
j x i= -k
k x j= -i
i x k= -j
A vector drawn from the origin to an arbitrary point P(x, y, z), is called a position vector defining the point P.
It is denoted by symbol r. In cartesian coordinate system
r = xi +yj + zk
Reference: These articles are referred from my authored book “concepts of electromagnetic field theory” having ISBN 978-81-272-5245-8. Try to make the figures for products of vectors. In case of any doubt in this article or any other EMFT or physics related article, kindly post in the comment section. Next time I will discuss the basics of cylindrical coordinate systems.