  The non-standard (Jordanian) quantum deformations of $so(2,2)$ and (2+1)
Poincar\'e algebras are constructed by starting from a quantum $sl(2,\R)$ basis
such that simple factorized expressions for their corresponding universal
$R$-matrices are obtained. As an application, the null-plane quantum (2+1)
Poincar\'e Poisson-Lie group is quantized by following the FRT prescription.
Matrix and differential representations of this null-plane deformation are
presented, and the influence of the choice of the basis in the resultant
$q$-Schr\"odinger equation governing the deformed null plane evolution is
commented.
