So the problem starts by defining 2-D cross product
$\vec u\times \vec v = u_1v_2 - u_2v_1$
Then it says "an alternative way to write this is..."
$$\vec u\times \vec v = \sum_{ij}^\ \epsilon ^{ij}u_iv_j $$
Where $\epsilon$ is defined as
$ \epsilon_{12} = 1$
$\epsilon_{21} = -1 $
$\epsilon_{11} = \epsilon_{22} = 0 $
Then it throws the 3D representation at me as
$$(\vec u \times \vec v)_i = \sum_{jk}^\ \epsilon _{ijk}u_jv_k $$
So they want the first 27 of this 3D sequence
Any explanation on the 3D representation would be helpful, I somewhat understand the 2D one