# When does it make sense to add numbers with different units?

Given two vectors containing numbers that have different natures / units, (example length in Meters and weight in Kilograms), does it make sense to calculate euclidean distance between these two vectors or cosine similarity?

The equations imply that you have to add $$meters^2$$ and $$kilometers^2$$ which supposedly does not make sense. Yet, I see this done many times indirectly, for instance, when calculating cosine similarity of documents based on tf-idf (vector that contains objects with dissimilar natures).