There is a way but it is very tedious if you have a bunch:
In perspective, set a CPlane perp to the end of the red line.
Project the blue line to the CPlane,
ProjectToCPlane > Copy=Yes, change its color
Set a Cplane 3Point to the end of the red line and the ends of the blue and projected blue lines.
ProjectToCPlane the purple line and change its color.
rotate3d along the red line, snapping to the Int of the curve you’re rotating and the projected blue line, then to the Int of the curve you are rotating and the projected purple line…
It IS tricky to get it right because of the way apparent intersection snapping works - you need to make sure the snap goes to the curve being rotated and not the line. I’ll see if I can come up with a better workflow.