We use polarized inelastic neutron scattering to show that the neutron spin resonance below $T_c$ in superconducting BaFe$_{1.9}$Ni$_{0.1}$As$_2$ ($T_c=20$ K) is purely magnetic in origin. Our analysis further reveals that the resonance peak near 7~m
eV only occurs for the planar response. This challenges the common perception that the spin resonance in the pnictides is an isotropic triplet excited state of the singlet Cooper pairs, as our results imply that only the $S_{001}=pm1$ components of the triplet are involved.
