If \(\mathbf{v}=2\mathbf{i}-\mathbf{j}+\mathbf{k}\) and \(\mathbf{w}=4\mathbf{i} +2\mathbf{j}-\mathbf{k}\), then using the definition of the cross product, we get \[ \begin{eqnarray*} \mathbf{v}\times \mathbf{w}&=&[(-1)(-1)-(1)(2)]\mathbf{i}-[(2)(-1)-(1)(4)] \mathbf{j}+[(2)(2)-(-1)(4)]\mathbf{k}\\[4pt] &=&-\mathbf{i}+6\mathbf{j}+8\mathbf{k} \end{eqnarray*} \]