list manipulation - Symbolically associate vectors and their norms

I am wondering how to handle the following situation: I do have vectors of known dimension that I would like to handle symbolically. I suppose I can do something like

avec = Array[a,2];
bvec = Array[b,2];

Now in my equations there are also scalars that represent the norms of these vectors, i.e. A == Norm[avec] So suppose I write an expression like

expr = A avec.(avec + bvec)

What I would like Mathematica to do is:

1. Whenever avec.avec is encountered, replace this by A^2


2. Whenever avec.bvec is encountered, leave this symbolic, don't expand into the elements of the vectors.

How can I achieve this?