Let's say a vector starts at Point P and points in the direction of v. How do I make sure that this vector exactly reaches the line? Its end should be exactly on the line, and not cross it.
You should calculate the intersection point (IP) between the two lines.
Solve the two equations and you get IP (X,Y).
Maybe you'd need to check that IP is between A and B... before continue...
Then you build a new line with this equation:
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