The vagueness is about what counts as dangerous within either of those two categories. If you said that a vague claim is one where it is uncertain what the speaker means, this is unacceptable because it is a definition which applies both to vagueness and ambiguity. As a result, this definition does not help to distinguish between the two terms. A dictionary is a book in which you look up words. A violent video game is one in which you blow things up.
Cooking is an exercise which involves preparing meals.