Azfar Mahmood, a senior piping designer, uses the following method in AutoCAD to select the intersection of two lines.
"When your crosshair selection box setting is small, finding the intersection of two dashed lines with the Intersection osnap can be tricky — especially if you are working so close to the crossing lines that you can't get the intersection. Zoom out slowly until you get the intersection. When you zoom in close to these lines, many times the crosshair selection box can’t find the intersection. When you zoom out, the crosshair selection box stays the same size, but the dashed linetype scales in view and can be selected, allowing you to use the Intersection osnap."
Notes from Cadalyst Tip Reviewer Brian Benton: I hate it when this happens; it’s frustrating. It also occurs when you are trying to trim lines but can’t select them because they are dashed. In both cases, zooming out typically solves the issue, but it can also make selection difficult because now there are more objects in the way.
Another osnap to try is the Apparent Intersection. This works great at one point of intersection. It pauses the command, allowing you to pick each line. AutoCAD then finds their intersection point and uses that. You could also try a Fence selection method as an alternative; type F on the Command line before making your section.