Calculate the angle between two vectors I come from Stack Overflow and I thought my question was more related to this forum. The problem is I'm not a mathematician, so please excuse me if my question is dumb.
I'm trying to get the angle between two vectors. As numbers of posts says, here or here, I tried this solution.
But my angle must be "oriented": If th angle between u⃗ and v⃗ is θ, the angle between v⃗ and u⃗ must be -θ.
Is there a mathematical solution to this?
Edit :
Here's the formula I implemented for the points $a = (x_1, y_1)$ and $b = (x_2, y_2)$ representing the vectors:
$$
\mathrm{angle} = \arccos \left(\frac{x_1 \cdot x_2 + y_1 \cdot y_2}{\sqrt{x_1^2+y_1^2} \cdot \sqrt{x_2^2+y_2^2}} \right)
$$

I assume $u$ and $v$ are both nonzero.
Let $\theta\in (-\pi,\pi]$ modulo $2\pi$ be the oriented angle between $u$ and $v$.
Using 
$$
\cos\theta=\frac{(u,v)}{\|u\|\|v\|}
$$
you can find the value of $\cos\theta$.
Taking $\arccos$ of the latter will, you get $\theta_0$ in  $[0,\pi]$ such that
$$
\theta=\theta_0 \quad\mbox{mod} \;2\pi\quad\mbox{or}\quad \theta=-\theta_0 \quad\mbox{mod} \;2\pi.
$$
Now to determine the orientation of $(u,v)$, you must compute the $2\times 2$ determinant of the matrix whose first column is $u$, and second column is $v$.
If this is $0$, this means $u$ and $v$ are parallel. Write $u=\lambda v$. If $\lambda >0$, then $\theta=0$ mod $2\pi$. If $\lambda<0$, then $\theta=\pi$ mod $2\pi$.
If the determinant is positive, this means $\theta=\theta_0$ modulo $2\pi$.
If the determinant is negative, you have $\theta=-\theta_0$ modulo $2\pi$.
