Finding default unit vectors in 3D modelling

[dr.fea]

When you are modelling elements like tubes, the local x-axis is defined along the tubes length.

If a unit vector for the z-axis is not applied, modelling softwares defaults to a coordinate system where the local zx-plane is parallel with the global zx-plane.

I'm not sure what that means exactly, since the zx planes obviously can't be literally parallel if the local and global x-axis isn't pointing in the same direction.

Could someone please explain? My goal is to make a transformation matrix from the default coordinate system to an arbitrary one, but since I don't see how the default one is found, I'm quite stuck..

 

[Unrest]

If a unit vector for the z-axis is not applied, modelling softwares defaults to a coordinate system where the local zx-plane is parallel with the global zx-plane.

Sounds like they mean to say the local z-axis is parallel to the global zx plane.

However, when the local x-axis is perpendicular to the global zx plane that rule can't define the orientation. The software must treat that case in some other way.