  We investigate for N = 3 supersymmetry (SUSY) in D = 2 the algebraic relation
between the Volkov-Akulov (VA) model of nonlinear (NL) SUSY and a
(renormalizable) SO(3) vector supermultiplet of linear (L) SUSY. We derive SUSY
and SO(3) invariant relations between component fields of the vector
supermultiplet and Nambu-Goldstone (NG) fermions of the VA model at leading
orders by using three arbitrary dimensionless parameters which can be recasted
as the vacuum expectation values of auxiliary fields in the vector
supermultiplet. Two different irreducible representations of SO(3)
super-Poincar\'e symmetry which appear in the same massless state are
compatible with each other in the linearization of NL SUSY. The equivalence of
a NL SUSY VA action to a free L SUSY action containing the Fayet-Iliopoulos
(FI) D term which indicates a spontaneously SUSY breaking is also discussed
explicitly according to the SUSY invariant relations.
