$$\begin{gathered} \mathrm{If} \stackrel{\rightharpoonup }{\mathrm{a}} \mathrm{and} \stackrel{\rightharpoonup }{\mathrm{b}} \mathrm{are} \mathrm{any} \mathrm{two} \mathrm{vectors} \mathrm{of} \mathrm{magnitudes} \\ 2 \mathrm{and} 3, \mathrm{respectively}, \mathrm{such} \mathrm{that} \\ \left|2\left(\overline{\mathrm{a}}\times \overline{\mathrm{b}}\right)\right|+\left|3\left(\overline{\mathrm{a}}.\overline{\mathrm{b}}\right)\right|=\mathrm{k}, \mathrm{then} \mathrm{the} \mathrm{maximum} \\ \mathrm{value} \mathrm{of} \mathrm{k} \mathrm{is} \end{gathered}$$