Definition:Position-Ratio of Point

Definition

 * Position-ratio.png

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.

Value of Position-Ratio
The value of the position-ratio can be expressed as follows: