$\vec{b}\times \vec{c}=\left| \begin{matrix} i \\ 2 \\ 0 \\\end{matrix}\,\,\,\begin{matrix} j \\ 0 \\ 1 \\\end{matrix}\,\,\,\begin{matrix} k \\ 1 \\ 2 \\\end{matrix} \right|=(-1,-4,2)$
$\vec{a}.(\vec{b}\times \vec{c})=(1,1,1).(-1,-4,2)=-1-4+2=-3$
$\left| \vec{b}\times \vec{c} \right|=\sqrt{1+16+4}=\sqrt{21}$
$3=\left| \vec{a}.(\vec{b}\times \vec{c}) \right|=\left| {\vec{h}} \right|\times \left| \vec{b}\times \vec{c} \right|\Rightarrow 3=\left| {\vec{h}} \right|\times \sqrt{21}$
$\Rightarrow \left| {\vec{h}} \right|=\frac{3}{\sqrt{21}}\times \frac{\sqrt{21}}{\sqrt{21}}=\frac{\sqrt{21}}{7}$