A while back I wrote a demo that presents standard Calc-3-textbook analytic geometry problems so that the user has to construct solutions in coordinate-free way using vectors, points, lines and planes: https://demonstrations.wolfram.com/ConstructingVectorGeometrySolutions/​The coordinate-free methods feel like "synthetic geometry," but I would accept that vectors, even as directed line segments, are an analytic tool. I've been gratified that a few people from around the world, who try to teach this sort of thinking in their classes, have contacted me and asked for mods for their use. It's been very few admittedly, but from around the world!, which has been very cool.
The demo broke once due to a non-compatible version update, and I've probably tweaked it for class from time to time. Here's an update, which I'm glad to share. The code is long, because it handles a large number of different kinds of problems. One can either execute the code at the end or use the following to download it from the internet:
In[]:=
(*alternativewaytoloadthevectorGeometryDemopackage*)​​Get["https://pastebin.com/raw/kgdeekKv"]
(*downloadsanotebookwiththecode*)​​NotebookPut@Import["https://pastebin.com/raw/hjMEuGm0","NB"];
A peek at the demo (it seems not to run well, or at all, in the cloud, but it's perfectly fine on the desktop):
In[]:=
vectorGeometryDemo[]
If the first argument of vectorGeometryDemo[] is True, then the user may enter their name to seed the random generator. I use this in class so that students get slightly different looks at a problem. It also records their name.
In[]:=
vectorGeometryDemo[True]
Full code of the package is attached to this post in a notebook named vectorGeometryDemo.nb

CITE THIS NOTEBOOK

Interactive vector Geometry exercises​
by Michael Rogers​
Wolfram Community, STAFF PICKS, September 23, 2024
​https://community.wolfram.com/groups/-/m/t/3279337