I can play video through streaming from youtube, but there is no option to like the video.
Is there any api provided by google or any other way to like the videos.
Google has released very recently the API of Youtube on Android, though it is still on an experimental phase. You can check it out here: https://developers.google.com/youtube/android/player/ (where some examples are also included).
You may also watch this video: http://www.youtube.com/watch?v=fhWaJi1Hsfo