Let OABC be a tetrahedron.The position vectors of A,B,C are $\widehat{i},\widehat{i}+\widehat{j},\widehat{j}+\widehat{k}$ respectively, O is the origin . consider the plane  ABC as base 

$height=\frac{3\left(volumeoftetrahedron\right)}{Areaof\Delta ABC}$

$volume=\frac{1}{6}\left|\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 0& 1& 1\end{array}\right|=\frac{1}{6}$

$A(1,0,0)B(1,1,0),C(0,1,1)$

$\overline{AB}=\hat{j}, \overrightarrow{AC}=-\hat{i}+\hat{j}+\hat{K}$

Area of triangle ABC=$\frac{1}{2}\left|\left(\overline{AB}\times \overline{AC}\right)\right|$=$\frac{1}{2}\left|\left(\hat{i}+\hat{k}\right)\right|=\frac{1}{\sqrt{2}}$