Point dividing Line Segment between Two Points in Given Ratio/Proof 1

Proof
We have that:
 * $\vec {A B} = \mathbf b - \mathbf a$

and so:


 * $\vec {A R} = \dfrac m {m + n} \paren {\mathbf b - \mathbf a}$

Hence the position vector $\mathbf r$ of $R$ is given by: