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  "body": "\n## Definition\n\nLet $n$ be a positive integer.\nA Euclidean vector in the [[Euclidean space|0XPR1E85W0]] $\\mathbb{R}^n$ is an element $v = (v_1, \\dots, v_n)$ of $\\mathbb{R}^n$. The real numbers $v_1, \\dots, v_n$ are the components of $v$.\nFor two points $A = (a_1, \\dots, a_n)$ and $B = (b_1, \\dots, b_n)$, the vector from $A$ to $B$ is\n$$\\overrightarrow{AB} = (b_1 - a_1, \\dots, b_n - a_n).$$\nThe sum of two vectors $u$ and $v$ is $u + v = (u_1 + v_1, \\dots, u_n + v_n)$.\nThe product of a real number $c$ and a vector $v$ is $c v = (c v_1, \\dots, c v_n)$.\nThe zero vector is $0 = (0, \\dots, 0)$.\n\n## Remarks\n\nTwo arrows give the same vector exactly when a translation moves one arrow onto the other.\nFor each three points $A$, $B$ and $C$, the vectors satisfy $\\overrightarrow{AB} + \\overrightarrow{BC} = \\overrightarrow{AC}$.\nWith the sum and the product by real numbers, the vectors of $\\mathbb{R}^n$ form a real vector space of dimension $n$.\n\n## Explanations\n\n### L1 human\n\nA vector tells you how to move: how far, and in which direction. The vector $(3, 4)$ in the plane says \"move 3 to the right and 4 up\". It does not matter where you start, so arrows of the same length and direction are the same vector.\n",
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