vector ops

(defun ⋅ (a b)
  "Compute dot product of two vectors."
  (assert (= (length a)
             (length b))
          (a b)
          "Cannot compute a dot product of ~S and ~S - lengths of vectors differ." a b)
  (reduce #'+ (map 'vector #'* a b)))

(defun × (a b)
  "Compute cross product of two 3D vectors."
  (assert (and (vector-3d-p a)
               (vector-3d-p b))
          (a b)
          "Cannot compute a cross product of ~S and ~S." a b)
  (make-vector-3d (- (* (vec-y a) (vec-z b))
                     (* (vec-y b) (vec-z a)))
                  (- (* (vec-z a) (vec-x b))
                     (* (vec-z b) (vec-x a)))
                  (- (* (vec-x a) (vec-y b))
                     (* (vec-x b) (vec-y a)))))