"A woman writes the book down by hand."
Translation:여자는 책을 손으로 씁니다.
I actually looked that up and found that 쓰다 is used when you use your brain and creativity to write something (a book, a letter, some calligraphy, lyrics, you name it), while 적다 is used for quite the opposite - when you don't think much, do it automatically, fast, maybe some sketch or scribble, things you don't care about much or when you talk about something written or reading what is written (just reading doesn't require a lot of brains). However, if you want to emphasize that what is written took some thought and creativity, then you use 쓰다. In a lot of situations, you can't tell what can be considered creative or not and it is rather subjective, so both words can be used interchangeably, but one should keep in mind their subtle meanings. I hope I explained it clearly :T
It can also be used to show which method you use. 빵을 칼로 잘라요. = Cut the bread with a knife. 영어로 말해요 = speak in (with) English.