This is the 4193rd most frequent Korean word.
줄은
"줄은" means "the line" or "the string" in English.
In this sentence, '줄은' is part of the expression '갈 줄은', indicating the speaker's lack of knowledge regarding the action of going hiking.
나는 내일 등산을 갈 줄은 몰랐어.
I didn't know I was going hiking tomorrow.
Here, '줄은' refers to a literal 'line' (줄), specifically indicating its position as the subject being in the bathroom.
까만 양말을 빨아야 했는데, 줄은 이미 목욕탕에 있었어요.
I needed to wash black socks, but the laundry line was already in the bathroom.
In this instance, '줄은' refers specifically to a 'line' (줄) and used to point it out while discussing its length.