Overloading (+)

The only way to overload a name in Haskell is to use type classes, so you have three choices:

• Make Vector an instance of Num and just have multiplication return an error.
• Use something like the numeric prelude, which defines more fine-grained numeric classes.
• Pick some other name like .+. or something similar for vector addition.

I know that I could make Vector3 an instance of the Num typeclass, but that is too restrictive for me; I do not want to define multiplication of a vector by another vector.

That would be the easiest solution, though. You can define multiplication as

(*)  =  error "vector multiplication not implemented"

Think of the vector operations that you would get for free!