I'm trying to solve a problem that is modeling a T shaped road intersection
There's three vectors that meet at a point, and I'm trying to pick the vector circled in orange (repersenting the intersecting road) out the three available ones. The only information given is three total directional vectors (one for each road)
Examples:
I currently tried finding the angle using the Angle between Two Vectors Formula to try to solve the problem
$$ \theta = \cos^{-1} \frac{\vec a \cdot \vec b}{| \vec a| | \vec b| } $$ but I have issues since it only covers 180 degrees not 360 degrees.
How can I approach and solve this problem? I'm trying to solve this problem in a C# program I'm writing.
Thanks