Farhad Kamangar 2017
In computer graphics a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point in 2 or 3-dimensional Euclidean space.
a point, $p$, in 2-dimensional space is represented tuples of numbers: $P = \left[ {\matrix{ x \cr y \cr } } \right]$
a vector, $v$, in 2-dimensional space may represent direction, normal to a surface, force, etc, and is also represented by tuples of numbers: $\overrightarrow V = \left[ {\matrix{ x \cr y \cr } } \right]$
The Cartesian coordinate systems in 3-dimensional space are either right-handed or left-handed
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a point, $p$, in 3-dimensional space represents a location and is presented by tuples of numbers such as: $p=\left[ {\matrix{ {{x}} \cr {{y}} \cr {{z}} \cr } } \right]$
a vector, $v$, in 3-dimensional space may represent direction, normal to a surface, force, etc, and is also represented by tuples of numbers such as: $\overrightarrow v=\left[ {\matrix{ {{x}} \cr {{y}} \cr {{z}} \cr } } \right]$