
Coordinate Systems
The space in which we live in, is threedimensional. In general terms, a dimension means a direction of movement of an object or a person. The 3 dimensions are :
I) moving or ,
II) moving or and
III) moving or
In the terminology of mathematics, the dimensions become a necessary (and sufficient) set of coordinates, required to uniquely specify the location of an object/ a point w.r.t a reference. The reference is known as the origin or pole.
For a 3D space, total number of coordinates required to specify a location is .
We have different coordinate systems, which specify location of a point w.r.t. origin.

Rectangular or Cartesian Coordinate System
The most intuitive coordinate system is the Cartesian Coordinate system. There are 3 mutually perpendicular axes, viz. , and . Their point of intersection is the origin. Each axis is a real number line, with origin indicating the number . Each coordinate of a point indicates the directed distance of the point from the origin, measured along respective axis. The directed distance can be negative or positive or 0.
The figure below is selfexplanatory.

Cylindrical Polar Coordinate System
A slightly advanced version is the cylindrical polar coordinate system. The coordinate is as it is in the Cartesian coordinate system. Remaining 2 coordinates are given by :
Alternatively, and .

Spherical Polar Coordinate System
A common observation is, almost all astronomical bodies are spherical (including earth). It is inconvenient to use the rectangular / cylindrical systems to specify the trajectory of objects moving along surface of such bodies. Hence, a new system has been introduced. It uses 2 angles and a distance as the coordinates.
is the distance of the point from the origin. The angle made by this line with positive axis is the angle . The other angle is , which is the angle made by the projection of point on plane with positive axis.
From the figure,
Note that, although can take values from to , to specify a point in 3D space, it is enough to vary it from to .

Distance and Section Formulas
Let and be any 2 points. The distance between them is given by
If divides in the ratio , then
sign, when divides internally, sign, when divides externally.
Note : Vectors are such an important tool in 3D geometry, that the analysis becomes way too simple!
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