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...
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...
Use the formula:
$\cos \theta = \frac{\vec {ab}\cdot \vec{ac}}{|\vec{ab}||\vec{ac}|}$
where $\theta$ is the angle between $\vec{ab}$ and $\vec{ac}$.
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: $\theta \;= \;\cos^{-1}\left(\frac{(\vec{ab})\cdot (\vec{ac})}{|\vec{ab}||\vec{ac}|}\right)$