Oriented line

In higher dimensions

In more general Euclidean space, ⁠${\displaystyle \mathbb {R} ^{n}}$⁠ (and analogously in every other affine space), the line L passing through two different points a and b is the subset $${\displaystyle L=\left\{(1-t)\,a+tb\mid t\in \mathbb {R} \right\}.}$$The orientation or direction of the oriented line (or directed line) above is from a reference point a (t = 0) to a target point b (t = 1), or in other words, in the direction of the relative vector b − a. A directed line is also called an axis, especially if it plays a distinctive role (e.g., an axis of rotation). Swapping points a and b yields the opposite directed line.