I have a rectangle that is randomly oriented in 3d space. I want to draw a line normal (perpendicular) to it. I can’t figure how to do it.
Easy:
1- Make a line on that face (that diagonal in my case)
2- Start a new line (the normal one) and keep the cursor like 1sec above the diagonal line endpoint in order for it to get the inference.
3- Move the cursor righly were the normal would point at (it will lock with this pink color)
4- Do the 2nd click to create the normal line.
Edit:
It actually gave me an idea of extension, such easy feature.
Thx for the insight 
Use the ‘Tape Measure’ tool and double click on that face. It will create a guide perpendicular to that face right where you double clicked. Use that guide to draw your edge.
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You don’t actually need an edge or a guide, one of the natural inferences is Perpendicular to face.
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Two more methods if you want to experiment with SketchUp:
1 - Pull or push the rectangle. Delete the new face that is parallel to the original rectangle. Draw your new edge using a parallel inference from one of the remaining edges or move a copy of one of these remaining edges to where you want, staying on the face for the move.
2 - Reposition the axes so that the red and green axes are on the face of the rectangle. Then, automatically, the blue axis will be perpendicular to the face. Use it to draw the required edge. Reset the axes when done.
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Have a look at this. Your specific query is demonstrates at around 4:30.
Guides, edges (‘Line’ tool) as well as a rectangles (to be pulled out) not only take advantadge of inferencing on a basic faces but also on faces inside (nested) objects to then create perpendicular directions. No matter whether the current axes have been rotated away from the system’s axes.