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Given two vectors $A$ and $B$ (with high dimension), and an angle $\alpha$. How can one find the vector $C$ which is $A$ rotated over $\alpha$ in the direction of $B$?

If it changes anything: the vectors $A$ and $B$ could be restricted to positive vectors.

Related questions:

Finding the rotation matrix in n-dimensions, Rotation matrices for arbitrary dimensions, High Dimensional Rotation Matrices As Product of In-Plane Rotations

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miselico
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1 Answers1

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Treat $A$ and the 'x axis' and $B$ (modified to make it orthogonal to $A$) as the 'y axis'.

Let $A' = {A \over \|A\|}$, $\tilde{B} = B-\langle A',B \rangle A'$, $B' = {\tilde{B} \over \|\tilde{B}\|}$.

Then the rotated vector is $\|A\| ((\cos \alpha) A'+ (\sin \alpha) B')$.

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