If $\mathbf{a} = \mathbf{i} + \mathbf{j} + 2 \mathbf{k}$ and $\mathbf{b} = \mathbf{i} + \mathbf{j} + 4 \mathbf{k}$
Compute the cross product $\bf{a} \times \bf{b}$.

$\bf{a} \times \bf{b}=$ $\bf{i}$ + $\bf{j}$ + $\bf{k}$