It sounds like you're trying to solve a Line-Plane Intersection problem. The solution is the point where the ray hits the floor plane.
Determining the distance between your begin point (at camera) and this intersection point will give you the length of your vector.
In JMonkey (which I'm not familiar with), it seems there are nice methods for finding collisions between two objects, provided that they are "collidable".
Collidable
The interface com.jme3.collision.Collidable declares one method that returns how many collisions were found between two Collidables: collideWith(Collidable other, CollisionResults results).
A com.jme3.collision.CollisionResults object is an ArrayList of comparable com.jme3.collision.CollisionResult objects.
You can iterate over the CollisionResults to identify the other parties involved in the collision.
Note that jME counts all collisions, this means a ray intersecting a box will be counted as two hits, one on the front where the ray enters, and one on the back where the ray exits.
See also: hub.jmonkeyengine.org/wiki/doku.php/jme3:advanced:collision_and_intersection
Then, as Glenatron said, you need to use the getContactPoint()
method of the collision to get the actual point in space. Your vector is then defined by the ray's point of origin, and the contactpoint.