Don't worry about the difference too much. In your examples 在 and 正在 show that an action is in progress. 在+verb is more common than 正在+verb, but they are both fine to say. There's only a small difference: 正在 emphasizes the action is happening now. i.e. A: 我们出去玩吧 - Let's go out and have fun! B: 晚一点吧，我正在吃饭呢 - Later! I'm eating right now. A:你看玩了没 - Did you finish reading it yet? B: 我正在看 - I'm reading it right now. Also, 在 is used as a preposition to state locations: 他住在美国 - He lives IN America. 我在超市- I'm AT the supermarket. 我们在图书馆里 - We're IN the library 杂志在电视机上 - The magazines are ON top of the t.v. 你的鞋子在沙发下面 - You're shoes are UNDER the couch.

as a complementarity, just like winni said "在" not only can be used "在+verb" to express past/Present Continuous Tense, but also express a place, for example: 我在北京--(i'm in BeiJing) 我在家-- (i'm at home/i'm in/i'm in home) 我正在北京((i'm in BeiJing now) 我正在家中 -- (i'm in home now)

我认为在与正在都是同一个意思，而在英语中，I`m eating ...翻译成中文是 我正在吃...或我在吃...因为这句话要表达的时候是 正在,现在时. 所以在翻译中才会出现 正在吃... 而在我们祖国,日常对话中是不会用到(正在...)的,而是用(在...) 但是,在书写或看文件的时候还是会用(正在...),正在一词表示强调那个时候,那个动作, 总的来说意思都是一样的.

基本上没有什么区别。通用。

我认为他们没什么不同，但是中国人很少这么说"我在做什么"，我们经常说"我吃饭呢" I think they are the same. but Chinese usually don't say like that , We regularly say "我吃饭呢" My English is poor, i hope you know my meaning.