They don't really run "in" your browser in the same way as a javascript or java program, but instead collaborate with it.
Basically they are seperate programs that get started up by the web browser
Sorry - that's not a really good answer as I haven't had to develop browser plugins myself and only have a basic understanding of what they do and how they work but it's enough to see how they can be written in any language - as they are binary code that's executed by the browser.
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