Learn Hardcore Norwegian: Jakken henger på kroken ved døren. - The coat hangs on the hook by the door.

Jakken means the jacket. In Norwegian you form the definite singular by adding -en (for masculine nouns) to the noun stem. Here jakke (jacket) + en = jakken (the jacket).

Why isn’t there a separate word for the before kroken and døren?

Norwegian uses enclitic articles (suffixes) instead of separate words. krok + en = kroken (the hook) and dør + en = døren (the door). You don’t need an extra the because the -en marks definiteness.

What does henger express in this sentence?

Henger is the present tense of å henge (to hang). It describes the state or position: the jacket is hanging. Unlike English, Norwegian often omits the auxiliary is and just uses henger.

How do the prepositions på and ved differ here?

På means on or at in contexts like placing or hanging something: på kroken = on the hook.
Ved means by, next to or beside: ved døren = by the door.

Could you say på døren instead of ved døren?

Yes, but with a different meaning.
På døren = on the surface of the door (e.g., a sticker on it).
Ved døren = next to or by the door (indicating proximity, not on its surface).

Why are all the nouns in the definite form (jakken, kroken, døren)?

Because we’re referring to specific, identifiable objects that both speaker and listener know about. In Norwegian you show that by using the definite endings -en, -a or -et depending on the noun’s gender.

How would you say a jacket is hanging on a hook by a door (indefinite version)?

Use the indefinite forms and articles:
En jakke henger på en krok ved en dør.
Here en is the indefinite article for masculine nouns, and jakke, krok, dør remain in their basic (indefinite) form.