>>791
(A×B)_i = ε_ijk A_j B_k

(A×B)・(A×B) = (ε_ijk A_j B_k) (ε_imn A_m B_n)
= (δ_jm δ_kn - δ_jn δ_km) A_j B_k A_m B_n
= A_m A_m B_k B_k - A_j B_j A_k B_k
= A^2 B^2 - (A・B)^2