Well, you could take solid white, than create the line with cropping that solid white using bezier mask.
Then animate that mask using keyframes.
That could work, if you have huge lot of time and patience.
Graham is right, this is not something to do in Vegas.
I would try Boris BCC Continuum Units 3D Objects which works well within Vegas. It is a very flexible plug-in. I have been experimenting with it and they have many tutorials on their web site. Of course it would all be done with key frames but I believe it is doable.