 Cylindrical basis

The local orthonormal basis associated with cylindrical coordinates: ${\mathbf{e}}_r=(\cos \theta ,\sin \theta ,0)$, ${\mathbf{e}}_{\theta }=(-\sin \theta ,\cos \theta ,0)$, and ${\mathbf{e}}_z=(0,0,1)$. The first two basis vectors depend on the angular coordinate and are undefined on the axis without a choice of angle.