Line

In ${\mathbb{R}}^2$, we define lines as $y=mx+c$

To describe a line, we need

1. A point on the line

2. A vector $\vec{d}$ in the direction of the line.

A line in ${\mathbb{R}}^n$ through a point $P$ with direction $\vec{d}$, where $\vec{d}\in {\mathbb{R}}^n$ is nonzero, is given by the vector equation $L:\vec{x}=\left[\begin{array}{c}{x}_1\\ ⋮\\ x_n\end{array}\right]=\overrightarrow{OP}+t\vec{d},t\in \mathbb{R}$