1.11 Prove the identities
(i) $(a \times b) \cdot (c \times d) = (a \cdot c)(b \cdot d) - (a \cdot d)(b \cdot c)$
(ii) $(a \times b) \times (c \times d) = [a, b, d]c - [a, b, c]d$
(iii) $a \times (b \times c) + c \times (a \times b) + b \times (c \times a) = 0$ (Jacobi's identity)