Hello! I am working on homework for my general relativity class, and I am very confused about how to tell the difference between spacelike, timelike, and null vectors, and the book is very unhelpful. Relevant equations Consider two four vectors a and b whose components are given by: a^α=(-2, 0, 0, 1) b^α=(5, 0, 3, 4) The attempt at a solution The book says: The length of a four vector is the absolute value of the space-time difference between its tail and tip. Four vectors that are spacelike have a tail and tip separation that is spacelike, timelike vectors have a separation that is timelike, and null vectors have null separation (length zero.) I think I can rule out that these vectors are null, since they don't have length zero, but how do I tell the difference between timelike and spacelike vectors? As you can see, the book is extremely unhelpful and I've looked all over for examples but I can't find any. The only thing I found that makes a little sense is that one has a positive scalar product and the other a negative one, but how can I use this to understand both vectors? I feel like this is a dumb question, but I hope you guys can help!