  A. Iosevich and K. Taylor showed that compact subsets of $\mathbb R^d$ with
Hausdorff dimension greater than $(d+1)/2$ contain trees with gaps in an open
interval. Under the same dimensional threshold, we prove the analogous result
where distance is replaced by the dot product. We additionally show that the
gaps of embedded trees of dot products are prevalent in a set of positive
Lebesgue measure, and for Ahlfors-David regular sets, the number of trees with
given gaps agrees with the regular value theorem.
