I know people have jumped here to try to explain it to you as a comment, but I highly recommend a recent talk by Freya Holmer. It's a fun little exploration of a seemingly simply question about vectors that motivates the answer you asked. It also culminates with an introduction to Clifford Algebras, which you may or may not want to learn about after the talk.
https://www.youtube.com/watch?v=htYh-Tq7ZBI