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If performance is not a concern, then you can create CLOS classes corresponding to vec3 or mat44, and dispatch the appropriate functions from the generic-cl project by specializing on them.
Good examples (perhaps a bit dated) of some of what you have in mind can be found in SB-CGA
If performance is a concern, then you would want to stick to CLHS provided simple-array and create appropriate types using deftype, and then dispatch on the types either by yourself, or by using something like polymorphic-functions and polymorph.maths.
If performance is a concern, then you would want to stick to CLHS provided simple-array and create appropriate types using deftype, and then dispatch on the types either by yourself, or by using something like polymorphic-functions and polymorph.maths.
If proper abstraction, type safety, as well as performance is important, then you might want to try out Coalton.