With three unit vectors $\vec{u}$, $\vec{v}$ and $\vec{w}$, where:
- $\vec{v}$ and $\vec{w}$ are strictly on the orthogonal plane of $\vec{u}$;
- in a left-handed coordinate system around $\vec{u}$.
How to get the angle from $\vec{v}$ to $\vec{w}$?
I know about the dot-product angle:
$$\cos \theta = \frac{\vec{v} \cdot \vec{w}}{\left|\left|\vec{v}\right|\right|\left|\left|\vec{w}\right|\right|}$$
but that gives the shortest angle despite the left-handed coordinate system.
