What is the correct preposition? (And is there one?)

I just stumbled upon a linguistic problem I wasn't able to resolve via web search. Suppose we're given some geometric set $A$ and subset $B\subset A$. Isn't there a compact way of saying that there exists, say, a plane whose intersection with $A$ is equal to $B$ of the form "there exists a plane intersecting $A$ (preposition) $B$"?

AFAICT, the prepositions "at", "by" and "along" do not fit in general. Maybe I refuse to accept that there is no such construction in English because I'm just too used to the analogous Russian expression.

• I use "in" for this. – Steven Landsburg Feb 3 '14 at 2:36
• Hmm... It seemed somehow off to me before. But now that you've mentioned it, it actually seems to be the one! =) – imakhlin Feb 3 '14 at 2:45
• I'd agree that "in" is correct, but potentially misread. Changing the quoted phrase in the question to "there exists a plane whose intersection with A is B" is unambiguous and scarcely longer than the more ambiguous. – paul garrett Feb 3 '14 at 3:01
• Although I use "in" for this all the time in conversations, I completely agree with @paulgarrett that for formal writing --- where there's no opportunity for the reader to ask for clarification --- it's much better to find a completely unambiguous construction. – Steven Landsburg Feb 3 '14 at 4:05
• It doesn't take too much remodeling to make this unambiguous: there exists a plane whose intersection with A is B. – Vidit Nanda Feb 3 '14 at 4:31