The second one is correct. In The quest opens up doors. the verb opens up agrees in person and number with the subject quest. The sentence doesn't require are if both the prepositional phrase of finding methods of expression and the restrictive relative clause that is authentic to oneself refer to the noun quest. The meaning of the sentence is that that quest which consists of finding methods ...
grammar - Which is grammatically correct? Open or opens? - English ...
The shop doesn't open in Wednesday, but it can open in a specific month (it opens in March) or year (it opened in 2012). For days we use on.
Opens on vs Opens in - English Language & Usage Stack Exchange
Open does not refer to any past event, while opened does. Both refer to the same current state, but opened opens the door to an earlier narrative, if you will. The door was once closed*, and someone or something changed it. The use of opened indicates a larger history for the object that open entirely ignores. *interestingly there is no aorist form of closed To get briefly technical, open can ...
Doing a quick search, some people have suggested that the term "opening hours" indicates the exact time that a business opens, whereas "open hours" indicates the periods of time that a business is open and ready to accept customers.
The elevator door can open on or to the fourth floor. Both are grammatical: The elevator door opens on the third floor, we emerge and walk our separate ways. (Google Books) The elevator door opens to the second floor. She looks back at the elevator. The tall suited man is still there. (Google Books) You're on the 4th floor waiting for the elevator. Does the door open on you or to you? When ...