I have vector $A$ and $B$, how do I find a vector $C$ that is orthogonal to $A$ and magnitude of $( B - C )$ is minimized?
2026-04-30 05:04:43.1777525483
adjust vector to be orthgonal
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The space of vectors orthogonal to $A$ represents a plane $\Pi$. You want a vector $C$ on the plane so that it is closest to $B$, this means you want an orthogonal projection of $B$ onto $\Pi$. This can be calculated by simply removing the $A$ component of $B$ as follows: $$C = B - \frac{B . A}{A . A} A$$