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  "body": "\n## Definition\n\nLet $n \\geq 2$ be an integer. A line in the [[Euclidean space|0XPR1E85W0]] $\\mathbb{R}^n$ is a set of the form\n$$L = \\{\\, p + t v \\;:\\; t \\in \\mathbb{R} \\,\\},$$\nwhere $p$ is a point of $\\mathbb{R}^n$. Here $v$ is a nonzero [[vector|0QN3D80AWP]] of $\\mathbb{R}^n$. The vector $v$ is a direction vector of $L$.\n\n## Remarks\n\nFor two distinct points $A$ and $B$, exactly one line contains both: the line through $A$ with the direction vector $\\overrightarrow{AB}$.\nThe point $p$ and the vector $v$ are not unique. The same line has each point of $L$ as a base point, and each nonzero multiple of $v$ as a direction vector.\nIn the plane $\\mathbb{R}^2$, the lines are also the sets $\\{(x, y) : a x + b y = c\\}$ with real numbers $a$, $b$, $c$ and $(a, b) \\neq (0, 0)$.\nIn the language of affine geometry, a line is an [[affine subspace|0PYW26VNT6]] of dimension 1.\n\n## Explanations\n\n### L1 human\n\nStart at a point $p$ and walk forward or backward in the direction $v$, for any amount of time $t$. The points you can reach form the line. For example, with $p = (0, 1)$ and $v = (1, 2)$ you get the line $y = 2x + 1$ in the plane.\n",
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