Straight Line

linear-algebra

Definition

Straight Line

A straight line is a straight one-dimensional figure that has no thickness and extends infinitely in both directions. It is defined by a set of points that align in a straight path, typically described in mathematics using linear equations or vector equations.

Vector Parametric Form

$$g:\vec{\omega }+\vec{\lambda }\cdot x$$

where

• $\omega$ is the position vector, pointing to the line and setting the offset of the line
• $\lambda$ is the rotation vector, setting the rotation of the line

Example:

Create a line in parametric form that passes through the points $P=(2,3)$ and $Q=(7,12)$.

$$g:\left[\begin{array}{c}2\\ 3\end{array}\right]+\left[\begin{array}{c}7-2\\ 12-3\end{array}\right]\cdot x$$

Note that the length of the rotation vector $\vec{\lambda }$ does not matter. Only its rotation.