$\overline{\mathrm{OA}}=6\overline{\mathrm{i}}+3 \overline{\mathrm{j}}-4\overline{\mathrm{k}}, \overline{\mathrm{OB}}=2 \overline{\mathrm{j}}+\overline{\mathrm{k}}, \overline{\mathrm{OC}}=5\overline{\mathrm{i}}-\overline{\mathrm{j}}+2\overline{\mathrm{k}}$ are the coterminous edges of a parallelepiped, then the height of the parallelepiped drawn from the vertex A is

Volume $=\left|\overline{\mathrm{OA}}\times \overline{\mathrm{OB}}\right|\times \mathrm{h}$

Volume $=[\overline{\mathrm{OA}} \overline{\mathrm{OB}} \overline{\mathrm{OC}}]=\left|\begin{array}{ccc}6& 3& -4\\ 0& 2& 1\\ 5& -1& 2\end{array}\right|$

$\begin{array}{rcl} & =& 6(4+1)-3(0-5)-4(0-10)\\ & =& 30+15-40=5\\ \overline{\mathrm{OA}}\times \overline{\mathrm{OB}}& =& \left|\begin{array}{ccc}\mathrm{i}& \mathrm{j}& \mathrm{k}\\ 6& 3& -4\\ 0& 2& 1\end{array}\right|=\mathrm{i}\left(11\right)-\mathrm{j}\left(6\right)+\mathrm{k}\left(12\right)\\ |\overline{\mathrm{OA}}\times \overline{\mathrm{OB}}|& =& \sqrt{121+36+144}=\sqrt{301}\\ \mathrm{h}& =& \frac{\mathrm{volume}}{|\overline{\mathrm{OA}}\times \overline{\mathrm{OB}}|}=\frac{5}{\sqrt{301}}\end{array}$