Some random comments to add to the confusion over this resolution question.....

Like others have said, vector files don't contain any resolution information. Those sorts of images print out at the resolution of the output device. So you won't find find any resolution settings for vector graphic output within their respective programs.

What you will usually find is a setting for the resolution of a screen image that can accompany your vector image. In the old days, vector images couldn't be previewed on the screen once they were brought into another program. The image eventually got rasterized in the printer so that it could be printed on paper. Fast forward to the future and, contemporary programs have the ability to display this screen image. Even if you choose a low resolution for your screen image, it will still print out at the resolution of your output device that can be much higher than what you chose for the screen image.

This screen image is also part of a "package" along with your vector file if you use a Postscript file format. Hence, the term ENCAPSULATED Postscript Image, or EPS.

Charles mentioned some settings that are in Illustrator with respect to resolution. Those are specifically for raster effects than can be applied in Illy. There's been a lot of added features to vector programs over the years that allow for the mixing of raster effects along with vector graphics. Things like drop shadows and blends generally look better rasterized as compared to vectors. So you can rasterize those sorts of effects in Illy and the resolution setting will only be applied to that raster effect, and the vector part of the image will go along for the ride at the output device's resolution. I'd suggest 300 ppi for that. If you save the file as a native Illy file then it will contain both vector and raster attributes that can be edited at a later time.

To continue the confusion, programs like Photoshop now also have some vector capabilities despite being a raster image editing program. So there's a lot of blending of capabilities between programs like Corel Draw, Photopaint, Illustrator, and Photoshop.

With respect to output, you eventually might have a need to export your mixed vector/raster type image. The results of what you get all depends upon the many output formats you might choose. Acrobat, for instance, will retain both the raster and vector characteristics if you so desire by choosing the proper settings. If you own the full version of Acrobat then you have very precise control over the resolution and compression of all sorts of image formats. But its only the raster formats that you can choose resolution- there are no such fields to choose resolution for any vector file formats. They simple use the term "images" to refer to raster images.

If you export out of a vector program as a jpg image then everything will be rasterized. If you stick with a Postscript image then that file format can also retain the vector and raster characteristics of your entire image.

For the nerds on this forum- the genius of most of these capabilities goes way back to two guys, Charles Geschke and John Warnock who were way ahead of their time with these concepts. Those two guys invented the Postscript printer language which still underlies the most popular graphics programs used in the world. Take a look at anything around you that's been professionally printed. It likely was designed on one of their programs. To this day, most people don't realize that if they send someone a MS Word document that it won't look the same on that person's computer unless they have the exact same fonts and monitor capabilities. That's why the Postscript printer language merged into the PDF file format that allows documents to be shared and look exactly the same on any platform.
You might know those two guys as the founders of Adobe Software.