Let AB be a line segment; then the point E is the internal division of AB in the ratio 1: k if

where $\overrightarrow{\mathit{\text{A}}\mathit{B}}$ is the vector from A to B. Alternatively E is the point $\frac{1}{1+k}$ of the way along from A to B. If A and B have position vectors a and b, from some origin, then the position vector of E is

sometimes referred to as the section formula. Compare external division.