I was discussing with a friend of mine whether the zero vector is parallel to all other vectors. We came to the conclusion that it probably is but we do not know the formal definition of parallel. What is the formal definition of parallel? Wolfram says that two vectors are parallel iff their cross product is zero. This, however, is meaningless if the vectors are of dimension greater than 3. While not the main point of the question, it would also be cool to know if there is some version of parallel for any vector space not just euclidean. Note: Since there are probably multiple definitions, give the one you think is most standard.