I have line RED that is not aligned with the axes.
The purple is a horizontal reference line.
How draw a line normal to Red such that the start and end have the same Z position. In other words, it would appear to be aligned with the purple line.
Set CPlane 3 points intersection of red and purple, and other end of purple, one end of red. Line>Perpendicular, start point intersection… is that what you want?
Edit - OK, I didn’t see you had a file attached in the first post, the above is not what you want. Maybe this:
In Front view, Line>Perpendicular, start from intersection, then type .y at the command prompt, and snap to the intersection again - then pull your line out and click to set the end.