Answer
$0 \times a=0=a \times 0$
Work Step by Step
Let $a=\lt a_1,a_2,a_3\gt$ and $0=\lt 0,0,0\gt$
$0 \times a=a \times 0$
$\begin{vmatrix} i&j&k \\ 0& 0&0\\a_1&a_2&a_3\end{vmatrix}=\begin{vmatrix} i&j&k \\a_1&a_2&a_3 \\0& 0&0\end{vmatrix}$
$(0a_3-0a_2)i-(0a_3-0a_1)j+(0a_2-0a_1)k=(0a_2-0a_3)i-(0a_1-0a_3)j+(0a_1-0a_2)k$
$0i+0j+0k=0i+0j+0k$
$0=0$
Hence, $0 \times a=0=a \times 0$
