First Common Lisp vector math code
Here are a few minor suggestions:


Use uninterned symbols instead of keywords in defpackage (e.g., #:neg instead of :neg) to avoid polluting the keyword package.
Fix your indentation.
Add a defgeneric with docs for each defmethod (you can fold defmethod inside defgeneric)
Decide if your objects are read-only; if they are, replace :accessor with :reader, if they are not, add mutator functions (e.g., scale in-place)
Rename norm to normalize (norm in math refers to the length of the vector)
Use (plusp x) instead of (&gt; x 0)
Use (/ x) instead of (/ 1 x)
In the else clause in norm can just return the argument or (create-vector3 0 0 0) for clarity