Answer
$a \times b=-7i+10j+8k$
and
$b \times a=7i-10j-8k$
Work Step by Step
$a\times b=\begin{vmatrix} i&j&k \\ 2& -1&3\\4&2&1\end{vmatrix}$
Expand along the first row:
$a\times b=\ i\begin {vmatrix} -1&3 \\ 2&1\end{vmatrix}-\ j \begin {vmatrix} 2&3 \\ 4&1\end{vmatrix}+\ k\begin {vmatrix} 2&-1 \\ 4&2\end{vmatrix}$
$a \times b=-7i+10j+8k$
$b\times a=\begin{vmatrix} i&j&k \\ 4&2&1\\2& -1&3\end{vmatrix}$
Expand along the first row:
$a\times b=\ i\begin {vmatrix} 2&1\\-1&3 \end{vmatrix}-\ j \begin {vmatrix} 4&1\\ 2&3 \end{vmatrix}+\ k\begin {vmatrix} 4&2\\ 2&-1\end{vmatrix}$
$b \times a=7i-10j-8k$
