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We construct and give a complete classification of all the differentialsymmetry breaking operators D_{{\lambda},{\nu}}^m : C^\infty(S^3,V^3_{\lambda}) \rightarrow C^\infty(S^2,L_{m,{\nu}}), between the spaces ofsmooth sections of a vector bundle of rank 3 over the 3-sphere V^3_{\lambda}\rightarrow S^3, and a line bundle over the 2-sphere L_{m,{\nu}} \rightarrowS^2. In particular, we give necessary and sufficient conditions on the tuple ofparameters ({\lambda}, {\nu}, m) for which these operators exist.

Conformally covariant differential symmetry breaking operators for a vector bundle of rank 3 over S^3