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We present new results based on high-resolution observations of Sgr A West at the Galactic center with the Very Large Array (VLA) at 1.3 cm. By combining recent observations with those made at earlier epochs with the VLA at wavelengths of 1.3 and 3.6 cm, we measured proper motions for 71 compact H II components in the central 80'' (3 pc, assuming D = 8 pc). Using VLA archival data for the H92α radio recombination line, we also investigated radial velocities in the LSR velocity range from +200 to -415 km/s. Combining proper motion and radial velocity measurements, we have determined the three-dimensional velocity distribution in Sgr A West. We find that the three ionized streams (Northern Arm, Eastern Arm, and Western Arc) in the central 3 pc can be modeled with three bundles of Keplerian orbits around Sgr A*. Assuming that each of the observed streams of ionized gas follows a single orbit, we determined the five orbital parameters (a, e, Ω, ω, i) for each of them using least-square fitting to the loci of the streams. The degeneracy in the orbital solutions for both the direction of flow and the two mirror images can be further resolved using the information obtained from the velocity measurements. Our results confirm earlier results on the streams in the Western Arc and the Northern Arm to be in Keplerian orbits, suggesting that the stream in the Eastern Arm is also consistent with an elliptical orbit. All three are confined within the central 3 pc. Both the Northern and Eastern Arm streams have high eccentricities (e = 0.83±0.10 and 0.82±0.05, respectively), while the Western Arc stream is nearly circular, with e = 0.2±0.15. All three streams orbit around Sgr A* in a counterclockwise sense (viewed from the Earth) and have orbital periods in the range 4-8x10⁴ yr. To verify the fit, the distributions of radial and transverse velocity vectors in Sgr A West were also computed using the Keplerian model and they show good agreement with both the proper motion and radial velocity data. In addition, the computed orbits suggest that the Northern and Eastern Arm streams may collide in the "Bar" region (a few arcsec south of Sgr A*) and that most of the orbiting ionized gas in the "Bar" region is located behind Sgr A*. We also report an ionized nebula associated with IRS 8, including a bow shock in radio continuum emission which shows excellent agreement with near infrared observations. From the H92α line data, we find evidence of substantial interaction between the IRS 8 nebula and the Northern Arm stream occurring in the bow-shock region. Other new morphological features revealed in our high-resolution image include (1) a helical structure in the Northern Arm, suggesting that MHD plays an important role in the motion of the ionized gas, in addition to the dynamics determined by the central gravitational field, and (2) a linear feature in the IRS 16 region, suggesting that the compressed edge of the Northern Arm may result from the collective winds and radiation pressure from the high mass stars in the IRS16 cluster.