Nikkor 35mm or 55-200mm? For better videos?

I have my nikon d5200 with 18-55mm kit lens. I want to go for any of the above lens. My requirement is to achieve good videos for travel videos or documentry.

If I should go for a prime, Should i consider 50mm 1.8g also?

I would carry my 18-55 mm lens for shooting most of the travel or documentary videos and have the 35 mm f/1.8 when I needed to shoot under low light, like at night or indoors. The 50 mm is just a little too long if you want to shoot documentary and travel. It is really a medium telephoto lens on your camera. You can see this if your set your 18-55 mm lens on 50 mm and look through your viewfinder

Nice.

35mm if you are shooting from a person's point of view. 55-200mm if you want to get nearer to the subject without really going there. You have to learn how to work with focal length before you can understand lenses.

Depends what sort of images you want to present, and your general style of filming. But I would be surprised if you did not want sometimes to see things which are quite a long way away, thus needing 200mm or longer. Likewise also surprised if the 35mm was not sometimes restrictive, and you wanted the wider end of the 18 to 55. 35mm is a slightly "long" normal lens on the D5100.

If you wanted video, you should've bought a Sony.

The 35mm lens will force you to work harder to get the shot because it doesn't zoom. This isn't a detriment, but actually a benefit in the long run because it'll teach you to be a better photographer. Another aspect of the prime is that it has a depth of field scale which allows you to easily set the aperture and focusing to achieve a specific depth of field (i.e. Hyper-focal focus). The much larger aperture will allow you to achieve that shallow DOF look not possible a with your kit lens.

The 55-200 is a completely different animal all together which, simply by offering different focal lengths, could be the best one to get. It all depends on what and how you shoot. If you need the long telephoto of the 55-200, then that is the one to get. Otherwise, the 35mm prime is giving you the ability to shoot in ways not possible with either lens.