We use inelastic neutron scattering to study magnetic excitations of the FeAs-based superconductor BaFe1.9Ni0.1As2 above and below its superconducting transition temperature Tc = 20 K. In addition to gradually open a spin gap at the in-plane antiferromagnetic ordering wavevector (1, 0, 0), the effect of superconductivity is to form a three dimensional resonance with clear dispersion along the c-axis direction. The intensity of the resonance develops like a superconducting order parameter, and the mode occurs at distinctively different energies at (1, 0, 0) and (1, 0, 1). If the resonance energy is directly associated with the superconducting gap energy ∆, then ∆ is dependent on the wavevector transfers along the c-axis. These results suggest that one must be careful in interpreting the superconducting gap energies obtained by surface sensitive probes such as scanning tunneling microscopy and angle resolved photoemission.PACS numbers: 74.25. Ha, 78.70.Nx Understanding the interplay between spin fluctuations and superconductivity in high-transition-temperature (high-T c ) superconductors is important because spin fluctuations may mediate electron pairing for superconductivity [1,2]. In the case of high-T c copper oxides, it is now well documented that the spin fluctuation spectrum is dominated by a collective excitation known as the resonance mode centered at the antiferromagnetic (AF) ordering wavevector Q = (1/2, 1/2) [3,4,5,6,7,8]. Although the intensity of the mode behaves like an order parameter below T c , the energy of the mode is dispersionless for wavevector transfers along the c-axis and directly tracks T c [4,5,6,7,8], thus suggesting that the mode is an intrinsic property of the two-dimensional (2D) CuO 2 planes and intimately associated with superconductivity. For FeAs-based superconductors [9,10,11,12], the presence of static AF ordering in their parent compounds (with spin structure of Fig. 1a) [13,14,15,16,17,18] and the remarkable similar doping dependent phase diagram to that of the high-T c copper oxides [15] suggest that AF spin fluctuations may also play an important role in the superconductivity of these materials. Indeed, recent neutron scattering measurements on spin fluctuations of powder samples of superconducting Ba 0.6 K 0.4 Fe 2 As 2 (T c = 38 K) [19] and crystalline electric field (CEF) excitations of Ce in CeFeAsO 0.84 F 0.16 (T c = 41 K) [20] found clear evidence for resonant-like magnetic intensity gain below T c athω ∼ 14 and 18.7 meV, respectively. However, the Ce CEF measurements give no information on the Q-dependence of the scattering [20]. Although the resonant-like scattering in Ba 0.6 K 0.4 Fe 2 As 2 occurs near the AF ordering wavevector, the powder nature of the experiment impedes to distinguish whether the resonant scattering is centered at the three-dimensional (3D) AF wavevector Q = (1, 0, 1) of its parent compound [16,17,18] or simply at a 2D AF in-plane wavevector Q = (1, 0, 0) [19].In this Letter, we report the results of inelastic neutron scattering studies of s...