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The central axis line of a well or a wellbore or a  pipeline with a position vector 

LaTeX Math Inline
body\bf r
at each point of of trajectory given as:

LaTeX Math Block
anchor1
alignmentleft
{\bf r} = {\bf r}(l)= \{ x(l), \, y(l), \, z(l) \}

...

LaTeX Math Inline
body{\bf r}(l)

position vector of  of trajectory points point with 

LaTeX Math Inline
bodyz(l)
being a ture vertical direction

LaTeX Math Inline
bodyl

path length from pipeline intake point 

LaTeX Math Inline
body{\bf r}_0

LaTeX Math Inline
body{\bf r}_0

well or pipeline intake point coordinates coordinates (usually  

LaTeX Math Inline
body\{ --uriencoded--%7B\bf r%7D_0 = \%7B x_0 = 0, \, y_0 = 0, \, z_0 = 0 \}%7D
)


In practice the trajectory is usually set by Deviation Data.

See also

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Natural Science / Physics / Measuring / Positioning 

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[ Deviation Data ] Trajectory DeviationInclination ]  [ Trajectory Azimuth ]