Say we have three $n$-dimensional vectors $A$, $B$ and $C$. Now let's say that $A$ and $B$ are symmetrical about $C$. In two dimensions, this seems to have a fairly obvious meaning, but for higher $n$, I'm not sure. What does this notion of symmetry mean in general?
2026-03-26 14:33:58.1774535638
What does it mean for vectors to be symmetrical?
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I would say it means $A$ and $B$ have the same length, that all three lie in the same 2-dimensional subspace, and the line through the origin and $C$ is the perpendicular bisector of the line segment joining $A$ and $B$.