"I see nothing because of the mist."
Translation:Ik zie niets door de mist.
This translation is confusing me. "Ik zie niets door de mist" translates to I see nothing through the mist, not because of - that would be vanwege :S
Both of them would be correct translations. "Door" has a few different meanings, and one of them is to describe a direct cause:
- Ik ben nat door de regen. - I am wet because of the rain.
"Vanwege" also translates as "because of", but it is more often used to describe a reason. In many cases, the two are interchangeable.
"Doordat" is always followed by a subordinate clause, so you need at least one verb behind it. In this case there is only a noun "de mist", so you cannot use it.
"Ik zie niets door de mist." (I see nothing because of the mist.) "Ik zie niets doordat de mist zo dicht is." (I see nothing because the mist is so thick.)
"Doordat" is a conjunction, while "door" is a preposition. A conjunction would start another clause, with its own verb, which is not the case here.