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  "body": "\n## Statement\n\nLet $a$, $b$ and $c$ be vectors in $\\mathbb{R}^3$. Let $\\times$ be the [[cross product|0N5N15HWZ7]] and let $\\cdot$ be the dot product. Then\n$$a \\times (b \\times c) = (a \\cdot c) \\, b - (a \\cdot b) \\, c.$$\n\n## Remarks\n\nThe formula is easy to remember as \"BAC minus CAB\": $a \\times (b \\times c) = b(a \\cdot c) - c(a \\cdot b)$.\nThe cross product is not associative. The formula gives $(a \\times b) \\times c = (a \\cdot c) \\, b - (b \\cdot c) \\, a$, which is in general different from $a \\times (b \\times c)$.\nA consequence is the Jacobi identity $a \\times (b \\times c) + b \\times (c \\times a) + c \\times (a \\times b) = 0$.\n\n## Explanations\n\n### L1 human\n\nThe vector $b \\times c$ is perpendicular to the plane of $b$ and $c$. A second cross product with $a$ gives a vector perpendicular to $b \\times c$, so the result lies back in the plane of $b$ and $c$. The formula tells you exactly which combination of $b$ and $c$ it is.\n",
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