# Relation between affine parameters

In Euclidean three-space with coordinates $(x,y,z)$ and line element

$$ds^2 = dx^2+dy^2-dz^2$$

It is easy to show using the geodesic equation that:

$x = lu+l'$, $y=mu+m'$, $z=nu+n'$

where $u$ is an affine parameter.

However, is it possible to find a relation between $l,m,n$?

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pervect
Staff Emeritus