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  "body": "\n## Definition\n\nLet $V$ be an inner product space over $\\R$ or $\\C$.\nTwo vectors $x, y \\in V$ are *orthogonal*, written $x \\perp y$, when $\\langle x, y \\rangle = 0$, where $\\langle \\cdot, \\cdot \\rangle$ is the [[inner product|0NB0AWGJBW]].\n\n## Remarks\n\nThe relation is symmetric, because $\\langle y, x \\rangle = \\overline{\\langle x, y \\rangle}$.\nThe zero vector is orthogonal to every vector, and it is the only vector orthogonal to itself.\nIn $\\R^2$ with the dot product, $(1, 2)$ and $(-2, 1)$ are orthogonal.\n\n## Explanations\n\n### L1 human\n\nOrthogonal is the general word for perpendicular.\nTwo vectors are orthogonal when their inner product is zero.\nIn the plane and in space, this means that they meet at a right angle.\n",
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