How can a vector have coordinates?

Question

If a vector is what carries a point to another point, and it can carry any point on a plane to another point on a plane, then how can it have coordinates ? shouldn't it be the "steps" needed to get the original point to the other point ?

Answer 1

Given what you say, you may see the vector's coordinates as the coordinates of the destination you'd reach if you started at the origin of the plane (i.e. $(0,0)$). This gives both:

• which direction it has
• how far it "goes"

which is all you need to define a vector.