Question

How do vectors represent a point in space?

Answer 1

Vectors don't normally represent a position, rather they represent a direction and magnitude. You can think of it as an offset or change. So if you subtract a point from another point, you get a vector. If you add a point and a vector, you get a point. You can add 2 vectors and get a vector. Adding points doesn't give you anything. Vectors are normally represented with <> and points are represented by ().

A position vector can represent a point in space. Suppose we have a vector `vec v=(a,b,c)` (sorry, can't seem to get <> working). You simply add the vector to the origin, which is a point. Since the origin is `(0,0,0)`, the position vector is `(a+0,b+0,c+0)` or simply `(a,b,c)`.