\begin{definition}[Definition:Position-Ratio of Point]
:thumb640px
Let $P$ and $Q$ be points in space.
Let $R$ be a point on $PQ$ dividing $PQ$ in the ratio:
:$PR : RQ = l : m$
where:
:$l$ is the length of the vector $PR$ in the direction of $PQ$
:$m$ is the length of the vector $RQ$ in the direction of $PQ$.
Then $PR : RQ$ is referred to as the '''position-ratio of $R$ with respect to the base-points $P$ and $Q$'''.
When $R$ is between $P$ and $QA$, the '''position-ratio''' is positive.
When $R$ is outside the segment $PQ$, the '''position-ratio''' is negative:
:one of the segments $PR$ and $RQ$ being positive and the other negative.
\end{definition}