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So, let's say I have vector $\vec{ab}$ and vector $\vec{ac}$. How do I calculate the amount of rotation from $b$ to $c$?

Note, this is in a 3D space, of course...

2 Answers 2

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Use the formula:

$\cos \theta = \frac{\vec {ab}\cdot \vec{ac}}{|\vec{ab}||\vec{ac}|}$

where $\theta$ is the angle between $\vec{ab}$ and $\vec{ac}$.

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    Oh, I see.. I apologize for my ignorance. :P It's late here and I'm tired.2013-01-01
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Let $\,\theta\,$ be the angle between the given vectors: $\,\vec{ab}\;\text{and}\; \vec{ac}\,.$

Recall that $\cos \theta\; = \;\left(\frac{(\vec{ab})\cdot (\vec{ac})}{|\vec{ab}||\vec{ac}|}\right)\;.$

Solving for $\,\theta\,$ gives us: $\theta \;= \;\cos^{-1}\left(\frac{(\vec{ab})\cdot (\vec{ac})}{|\vec{ab}||\vec{ac}|}\right)$


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    That's correct, Steven - typo (mind wandering: just answered a question on transitivity: $(a, b) \land (b, c) \implies ...$). The angle of rotation to get from b to c is the angle between $\vec {ab}$ and $\vec {ac}$2013-01-01