We all know that we can divide a line both internally and externally in some ratio. I can relate the concept of internal division of a line to the real world but does the concept of external division of a line have a physical meaning in the real world and if so what is it?
Any help is appreciated.
You can use external division in physics. Suppose you have forces that depend on the distance, one attractive and one repulsive (say you have an electric field generated by a positive and a negative electric charges, of different magnitude, some distance $R$ apart). Then the equilibrium position is given by the external division. The ratio is equal to the square root of the magnitude of the charges.