Would one tripod work on all the different brands of cameras and camcorders?

I have a Vivitar tripod and the number next to "Vivitar" is VPT-120. The camcorder I have is a Sony and the model number is DCR-TRV830. Would I need a specific tripod for that, the tripod I currently have doesn't appear to be working. What tripod should I purchase? Approximate cost? Sources?