If $\overline{\mathrm{u}}=\overline{\mathrm{a}}-\overline{\mathrm{b}}, \overline{\mathrm{v}}=\overline{\mathrm{a}}+\overline{\mathrm{b}},\left|\overline{\mathrm{a}}\right|=\left|\overline{\mathrm{b}}\right|=2$ and $\overline{\mathrm{a}}.\overline{\mathrm{b}}=3$ then $\left|\overline{\mathrm{u}} \mathrm{x} \overline{\mathrm{v}}\right|=$

$$\begin{gathered} \overline{\mathrm{U}}\times \overline{\mathrm{V}}=(\overline{\mathrm{a}}-\overline{\mathrm{b}})\times (\overline{\mathrm{a}}+\overline{\mathrm{b}}) \\ =\overline{\mathrm{a}}\times \overline{\mathrm{b}}-\overline{\mathrm{b}}\times \overline{\mathrm{a}}=2(\overline{\mathrm{a}}\times \overline{\mathrm{b}}) \\ |\overline{\mathrm{U}}\times \overline{\mathrm{V}}|=2|\overline{\mathrm{a}}\times \overline{\mathrm{b}}| \\ |\overline{\mathrm{a}}\times \overline{\mathrm{b}}{|}^2=|\overline{\mathrm{a}}{|}^2 |\overline{\mathrm{b}}{|}^2-{(\overline{\mathrm{a}}·\overline{\mathrm{b}})}^2 =4\times 4-9=7 \\ |\overline{\mathrm{a}}\times \overline{\mathrm{b}}| =\sqrt{7} \\ |\overline{\mathrm{U}}\times \overline{\mathrm{V}}|=2\sqrt{7} \end{gathered}$$