Given $(a, b) R (c, d) \implies ad(b - c) = bc(a - d)$.

Symmetric:
$(c, d) R (a, b) \implies cb(d - a) = da(c - b)$. This is symmetric.

Reflexive:
$(a, b) R (a, b) \implies ab(b - a) \neq ba(a - b)$. Thus, not reflexive.

Transitive:
$(2, 3) R (3, 2)$ and $(3, 2) R (5, 30)$ but $((2, 3), (5, 30)) \notin R$. Thus, not transitive.

Therefore, R is symmetric but neither reflexive nor transitive.