Word embeddings are widely use in several applications due to their ability to capture semantic relationships between words as relations between vectors in high dimensional spaces. One of the main problems to obtain the information is to deal with the phenomena known as the Curse of Dimensionality, the fact that some intuitive results for well known distances are not valid in high dimensional contexts. In this thesis we explore the problem to distinguish between synonyms or antonyms pairs of words and non-related pairs of words attending just to the distance between the words of the pair. We considerer several norms and explore the problem in the two principal kinds of embeddings, GloVe and Word2Vec.