Write a 3D vector r = xi + yj + zk in column matrix form [r) = y (in quantum mechanics we call it "ket vector"), and we define a corresponding "bra vector" (r| = (x y z) (i.e. it is a row matrix). Then the ordinary dot product can be written as A . B = (A|B) and vector product between two vectors A = Axi + Ayj + Azk , and B = Bxi + Byj + Bak can be written in matrix 0 -Az Ay BY form |A x B) = Az 0 -Ax By Using this matrix form of vector product to prove -Ay Ax 0 Bz Ax [B) the 3D vector identity A x (B x C) = B(A . C) - C(A . B)