My lecturer occasionally writes his position vectors as a matrix, as follows:

$\displaystyle \vec{r} = \left( \begin{array}{ccc}

0 & -r_z & r_y \\

r_z & 0 & -r_x \\

-r_y & r_x & 0 \end{array} \right) $

Where does this come from? Why does he use it? Is it equivalent to $\displaystyle \vec{r} = \left( \begin{array}{ccc}

r_x \\

r_y \\

r_z \end{array} \right)$

For example, he uses it in deriving Newton's 2nd Law for Rotational Motion, as I have attached as a JPEG.