Vector based programs are the medium for vector artwork which can be done in a multitude of different techniques. Making Vector a "style" while Adobe Illustrator, for example, is a medium.
Although you've explained yourself well, vector is a medium and not a style. A style dictates the visual element of it, however vector is the medium as it's what it is made of.
Looking at the points you've raised:
Adobe Illustrator/Photoshop/Corel Draw/Inkscape etc... would be the tool you use to create the art. Similar to using a paintbrush or biro. You create the work with the program.
Devious Comments
I hope you've got each one of them right!
I think you should give the correct answer only after the poll is over, imo.
Looking at the points you've raised:
Adobe Illustrator/Photoshop/Corel Draw/Inkscape etc... would be the tool you use to create the art. Similar to using a paintbrush or biro. You create the work with the program.
I hope this helps