How to move a node along a vector?

I have a bunch of nodes in a circle around a centre point. I got these positions by drawing arcs first then using the arcs [X,Y] position, populated an array which was used for the positions of the nodes. Using the forcelayout from the javascript library D3.

What I want to do now, if the nodes meet a certain criteria, for example, name starts with L, move them out to the outline of a bigger circle. I have made a simple diagram to explain.

I wish to be able to move from [X2,Y2] to [X3,Y3]. I labelled [X1,Y1] as I am sure you would need this to work out the vector from x1y2 to x2,y2 wish would then be used to calculate the movement along that vector, but I'm unsure how to do this movement

I don't know if the problem is still active, but I'll answer anyway. Since the Problem has a cylindrical symmetry it is best to use polar coordinates. So x,y become r,phi whereas r = sqrt(x^2+y^2) and phi=arctan(y/x). If you want to move a point X(r,phi) in the radial direction by lets say r' you do it by simple adding it to the existing radius. Thus X'=X(r+r',phi)