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  "body": "\n## Summary\n\nA vector-valued function is a [[function|0EPAT51DXQ]] whose values are vectors, for example $f \\colon D \\to \\mathbb{R}^m$ with $D \\subseteq \\mathbb{R}^n$ and $m \\ge 2$.\nSuch a function has $m$ component functions $f_1, \\dots, f_m \\colon D \\to \\mathbb{R}$, with $f(x) = (f_1(x), \\dots, f_m(x))$ for each $x \\in D$.\nAn example is $r(t) = (\\cos t, \\sin t, t)$ for $t \\in \\mathbb{R}$, whose values trace a helix in the [[Euclidean space|0XPR1E85W0]] $\\mathbb{R}^3$.\n\n## Remarks\n\nLimits, continuity and derivatives of a vector-valued function into $\\mathbb{R}^m$ can be computed one component at a time.\nWhen the domain is an interval of $\\mathbb{R}$, the function is a [[parametrised curve|0G7WM8DX4P]].\n\n## Explanations\n\n### L1 human\n\nA vector-valued function gives an arrow, or a point, for each input, not a single number.\nIf $t$ is time, then $r(t)$ can be the position of a moving particle in space.\n",
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