The first way is to draw two lines to represent your plane. Then draw in your lines extending to anywhere. Now, we'll use the intersection point of the line and plane as the first coordinate for whichever command we choose. If we want a line with its first point as that coordinate then use the line command, then when it asks for the first point type:
You now choose the end points of the line first (it doesn't show the snap icon, but it's working), then choose the three end points of lines for your plane. The line you're drawing will now start at the intersection point of line and plane.
However, I'd find it quicker to create a solid (box, perhaps) with the edge in the same position as the lines I want, then slice them using the 3 points of the plane. Then just draw over the appropriate edge.