[en] It is shown that the unification of 3+1 families is possible within the framework of 64 dimensional spinor representation of SO(14). Special care is given for a description without the heavy excess fermions such as conjugate and mirror or completely exotic fermions of some family unification schemes. With the aid of an intrinsic ''L-R Asymmetry'' mechanism which we proposed recently, the conventional strong and electromagnetic interactions are obtained for all four families by concentrating only on the symmetry breaking SO(14) → SU(3)sub(c) x U(1)sub(e.m.). However, the conventional weak interactions of the first three families are obtained just as in the standard SU(2)sub(L) x U(1)sub(Y) model, while those of the prescribed fourth family show certain differences. This is what we mean by 3+1 family unification. All vector particles mediating strong, electromagnetic and weak interactions which are the subjects of present phenomenological tests are specified among the vector fields of SO(14) and their mass mechanisms leading to a consistent description of this low-energy phenomenology are studied with the aid of the Higgs multiplets 14, 364, 1716 and 2002 of SO(14). Moreover, the fermion mass mechanisms are considered with the aid of these scalar multiplets and the contributions from these scalars to the vector and fermion masses are explicitly calculated. All these calculations are carried out in the new mathematical technique for the Lie algebra representations which we introduced recently. (author)