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Mathematics-Online lexicon:

Cartesian Coordinate System in the Plane and in Space

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A Cartesian coordinate system in the space consists of $ 3$ number lines (axes) perpendicularly intersecting in one point $ O$ called the origin. The orientation of the axes is chosen according to the ,,Right-Hand-Rule`` as shown in the figure.

\includegraphics[width=.4\linewidth]{kartesische_koordinaten_en} $ \quad$ \includegraphics[width=.4\linewidth]{rechte_hand_regel_en}

A point $ X$ is determined by the values $ x_i$ - called the coordinates - obtained by perpendicular projection of the point $ X$ onto the axes: $ X=(x_1,x_2,x_3)$ . Using a notation without subscripts, the coordinates are usually symbolized by $ (x,y,z)$ and the number axes are called $ x$ -, $ y$ - and $ z$ -axis.

A Cartesian coordinate system in the plane is defined in an analogous manner.

see also:

[Examples]
  automatically generated 3/17/2011