What is the angle between the extension of a vector and another one intersecting one with it?

Question

Imagine 3 points (p1, p2 and p3) in 2D plane, we have the vectors starts from p1 to p2 and a second vector starts from p2 to p3 . What is the angle between the extension of the first vector and the second vector. I'm wondering if there a general formula to find such angle in any quadrant looking

Answer 1

Express the 2 vectors A and B in Cartesian coordinates.  The angle between them is just

 

θ = cos^-1(A·B / |A||B|),

 

where

 

A·B = A_xB_x + A_yB_y + A_zB_z

|A| = √(A_x² + A_y² + A_z²)

|B| = √(B_x² + B_y² + B_z²)