angle between $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ is $60^{\circ} .$
$\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$ is $\perp^{\mathrm{r}}$ to plane containing $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$
$\vec{c}=\vec{a}+2 \vec{b}+3(\vec{a} \times \vec{b})$
$\overrightarrow {\rm{c}} = |{\rm{\vec a}}{|^2} + 4|\overrightarrow {\rm{b}} {|^2} + 2.2|{\rm{\vec a}}{|^2}\cos {\rm{ }}60^\circ {\rm{ }}{{\rm{n}}_1} + 3|{\rm{\vec a}}|||\overrightarrow {\rm{b}} |\sin {\rm{ }}60^\circ {\rm{ n}}2$
$+||3 \overrightarrow{\mathrm{b}}|| \overrightarrow{\mathrm{b}} | \sin 60^{\circ} \cdot \overrightarrow{\mathrm{n}} 2$
$\overrightarrow{\mathrm{n}}_{1} \perp^{\mathrm{r}} \overrightarrow{\mathrm{n}}_{2}$
$|\vec c{|^2} = (1 + 4 + 2) + 9 \times \frac{3}{4}$
$|\overrightarrow{\mathrm{c}}|^{2}=7+27 / 4=55 / 4$
$2|\overrightarrow{\mathrm{c}}|=\sqrt{55}$
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