Computing Cross Product from Column Matrices

Say that the vector u is represented by     u   =   (u_i , u_j , u_k )^T
and that the vector v is represented by     v   =   (v_i , v_j , v_k )^T.

Then   u × v   =   ( u_j v_k - u_k v_j ,   u_k v_i - u_i v_k ,   u_i v_j - u_j v_i )^T.

There is a pattern in how this is formed. Look at it a bit. But don't even think of memorizing it.