depends. For ray-tracing, the rays originate from the camera viewpoint. For collision detection, they are the position of a particle when you fired a ray (like the muzzle position of your gun when firing a bullet). Rays are usually starting from a position, as you say, and can have a maximum length. They can be defined by two end points, like a segment in 3D space.

Theoretically, a ray can be totally infinite, and have no start position. It''s just an equation. Like planes, that extend to infinity. They can be totally abstract. Although A ray with no frame of reference seems to be unpractical.

the equation for solving a ray-plane intersection is

t = ((APointOnPlane - APointOnRay) * PlaneNormal) / (RayDirection * PlaneNormal).

so, the point on ray and the point on plane can be anything (on the plane and the ray, respectively, of course). ''t'' will tell you how far the plane is from PointOnRay along the RayDirection, and the point of intersection is then

PointOnPlaneAndRay = APointOnRay + RayDirection * t

so you do need a frame of reference at some stage. Note that, for the equations above, RayDirection does not need to be a unit vector (of magnitude = 1.0f), but it''s more practical to use a unit length vector most of the time.

Technically all rays have a start point. When they are entirely infinite we call them lines

I think you should post such threads in the math/physics section.
BTW that''s really trivial 3D maths. Read what''s already available in Gamedev before asking such simple questions. They have so many tutorials for beginners.