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Is there an option to first line up an axis of the 3D cursor to be parallel to an imaginary line passing through two selected vertices, then without losing that relationship to line up a second 3D cursor axis with another set of selected vertices.

I want to find a method to setup an arbitrary coordinate system quickly at any moment. Take the picture below for example. I snapped the 3D cursor to the vertex I wish to move. Is there a way to set the cursor's rotation so that one axis is parallel to an imaginary line that passes through the vertex closest to the 3D cursor and the last selected vertex while another 3D cursor axis is set parallel to an imaginary line that passes through the other two vertecies?

[enter image description here

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This sounds needlessly complex. This problem can be solved with moving a point on the line and selecting it when it is needed.
You want the cursor on any point P on given line L.

  1. in vertex select mode , select line
  2. right click > subdivide line, you will have point P now.
  3. move point P by pressing g twice , this will move it along the line (And make the line yellow), place this on the line where you need the cursor to go. If you need exact number you can use .5 and -.5 to go 1/4 or 3/4 of the way on the line from the middle.
  4. Shift +S snap cursor to selected
  5. (optional) select point P , then one of your line vertices, F3> Merge > at Last , this will merge your vertex in when you are done with it.

If you need other "imaginary lines" you can use this method , build temporary (2 verts then f ) lines, and then delete the temporary lines when you are done lining up things.

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