2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61565The tensor product of vector and arbitrary representations of the nonstandard q-deformation U'_q(so(n)) of the universal enveloping algebra U(so(n)) of Lie algebra so(n) is defined. The Clebsch-Gordan coefficients of tensor product of vector and arbitrary classical or nonclassical type representations of q-algebra U'_q(so(n)) are found in an explicit form. The Wigner-Eckart theorem for vector operators is proved.16 pages, LaTeXQuantum AlgebraMathematical Physicstext