Relative Newbie Question: I have Civil War earthworks tied to the State Plane Coordinate system with a jpeg of the terrain as a 100k scale USGS Quad of the area that is not georeferenced. When I work with the features in CAD, they all have georeferences. But when I export the shapefiles out of CAD and into QGIS, all of the shapefiles come into QGIS where they should be. BUT, the jpeg is not only not under them, but it is 10x larger than it should be and displaced by some absurd difference. Can anyone shed some light on what I'm not doing in order to get them all into one area and at the right size?
JPG is not a spatially aware raster format, and the process by which different programs independently georeference rasters and save that transformation information doesn't necessarily transfer. I see two potential options. In CAD export the image as a georeferenced tif file (you may or may not be able to do this depending on what software you have), or alternatively redo the georeferencing directly in QGIS. See How to align (georeference) images using QGIS? or this tutorial for that.
The reason the image is so large is that a pixel is counted as a raster cell, and cell size can be defined. If not defined (ie, in a spatially aware format or reference file), it is assigned by the software and rarely correct. And of course the reason it's in the wrong place is there's nothing in a jpg to tell GIS where the right place is.
Also, I'm assuming you say the shapefiles are where they are supposed to be as confirmed by other data or basemaps. While the process you generally describe could/should allow your CAD data to be correctly projected, if you're not actually comparing it to anything other than itself there is a possiblity it, too, is not in the correct place. Much of that depends on knowing Vectorworks and how those tools work, which I do not. Therefore I have to solve from the other direction (not that I'm a QGIS expert, but more from the GIS side than from the CAD side).
Step one would be to go into Vectorworks (or QGIS, having just loaded the layer and done nothing else) and find the coordinates of a point. If it's in the hundreds of thousands x/y value, it probably is state plane. If not, you have a different problem. Step two is to go into QGIS and for each one of those vector layers (as they come in, don't move anything) define the projection to whatever state plane you're using (see also this alternative information page). QGIS knows the values of the coordinates but not what they are referring to, and by defining the projection you establish where the x/y origin should be among many other things. As an aside, if you're exporting actual shapefiles (.shp) from Vectorworks and the data truly is georeferenced to state plane, it really should be saving a prj file that defines what projection the data is in.
Once you have your vector lines in the right place, then you can load your image in and georeference it as above. I don't know how Vectorworks stores the info for a georeferenced image, and whether those files can be used by QGIS to get it into the right place - and this is making the assumption you had the image file referenced in Vectorworks to begin with; I might have misinterpreted your original post. You definitely don't want to move either your image or your vector lines to match the other unless you know whatever you're matching is for sure in the right place. I suggest using an additional base layer from somewhere (ie, find a PLSS grid from the county or BLM, as your topo map is going to have multiple sections at that scale) to get your control points for referencing and/or verifying your data is where it should be and you think it is. Also note that georeferenced images rarely line up exactly with other spatial data unless they've been orthorectified or are the source it's been digitized from.