Somebody hand me a can opener
I'm guessing "balance vector" is the problem.
The balance vector is the result of adding together all the forces acting on the skier. The centrifugal force in a turn acts to pull the skier out of the turn. Gravity to pull them down. Snow friction to push the skiis back. Air / wind resistance to push on the body. When you add all of these together, you get a net force, acting on the center of mass (CM), pulling the CM in a particular direction.
You can draw this force as an arrow, with a tail at the CM and head pointing directly in the direction this net force is pulling.
The Base of Support is the entire area between all points touching the snow that support the skier.
If you orient the base of support so that this balance vector is pointing into it you will stay upright. It does not matter where in the base of support the net force is pulling the CM (ie, the balance vector points). It matters only that this balance vector is pointing somewhere into the base of support.
You can look at all the force as vectors, and add them up, by putting the tail of one to the head of another, like a chain.
This might help: -- the money shot --
which is http://www.ronlemaster.com/images/20...ce-width-A.jpg
The green arrow is the resultant of the yellow and blue arrows; it is the balance vector. For simplicity, it ignores snow friction and air resistance. It points into the base of support -- directly to the inside edge of the outside ski.
That shows Herman's weight to be over a very dominant outside ski.
If the green arrow went between the legs, the balance point would be between the feet, and you'd see both skis decambering. In this photo, it looks like weight is just starting to be applied on the inside ski, as it's nearly straight. Perhaps the green arrow is not in exactly the right place, but, close enough.
If the green arrow pointed further to the outside, he'd rise up, the edge angles would diminish and the turn would straighten. That alone could reduce the centrifugal force (represented by the blue arrow) so that the balance vector continued to point into the base of support, and he'd continue skiing.
If it continued to point outside, he'd continue to rise and go right over.....he would not be in balance.
He'd have to re-orient the base of support so that the balance vector points into it again, or fall.