HTC vive
HTC vive
CPU will be fine but I don't think the 1050Ti is VR capable. Take it from someone who owns the Vive, it sucks if you run it with minimum specifications. The Vive has scaleable resolution and many games use scaling graphic systems now, so at minimum specs all the games just look like shit, it's not worth it. If your interested in a vive, i'd reccomend a minimum of a 1060.
Everything should function properly. The performance will be satisfactory. I've also tested a Rift from a 7970, so it should work without issues.
Given your less powerful graphics card, choosing an Oculus Rift would be more suitable due to its ASW capability. This model supports smoother performance on less capable PC systems compared to the HTC Vive. The GTX 1050 Ti satisfies the Rift’s minimum specs, while falling short for the Vive.
Your CPU should handle it just fine. I used a Phenom II from 2009 with smooth performance and no frame drops. For VR, a minimum of a 1070 is ideal. Any slowdowns are really bad in virtual reality. Adding Super Sampling to most games improves clarity and visuals significantly. Switching from 1070 to 1080Ti made a noticeable difference in performance and sound quality. You can still play the Vive on a 1060, but expect only average results, especially in tough games like Raw Data. The SteamVR test app is a useful tool for checking performance.