In order to find the similarity between words, cosine similarity seems to be the most common measure to use. In a conversation that I had about this topic, someone mentioned that words that mean more or less the same, such as 'big', 'huge' or 'gigantic' would have a high similarity (small angle), yet due to the difference in frequency of the words in the text, the magnitude of the vector might be different. It was said that the vectors associated to words that are common, would have a higher magnitude.
Is is true that the magnitude of a word vector increases as its associated word appears more frequently in a text? And if so, how can this be explained?