Coordinates of $P,Q,R$ are $\left(r_1,-r_1+1,2r_1-2\right),$ $\left(2r_2,r_2+1,r_2-2\right),$ $\left(-r_3,-r_3+1,r_3-2\right)$ respectively.
It must satisfy the plane, hence $r_1=\frac{3}{2},r_2=\frac{-3}{2}{,r}_3=+1.$ So points $P,Q,R$ are $\left(\frac{3}{2},-\frac{1}{2},1\right),\left(-3,-\frac{1}{2},\frac{-7}{2}\right)$ $\left(–\mathrm{1,0},–1\right)$ respectively.
$\overrightarrow{PQ}=-\frac{9}{2}\widehat{i}-\frac{9}{2}\widehat{k}$
$\overrightarrow{PR}=\frac{-5}{2}\widehat{ı}+\frac{1}{2}\widehat{j}-2\widehat{k}$
Area $=\frac{1}{2}\left|\overrightarrow{PQ}\times \overrightarrow{PR}\right|$
$=\left|\frac{1}{8}\right|\left|\begin{array}{ccc}i& \hat{j}& \hat{k}\\ -9& 0& -9\\ -5& 1& -4\end{array}\right|$

$=\frac{1}{8}\left|\begin{array}{ccc}9\hat{i}& +9\hat{j}& -9\hat{k}\end{array}\right|=\frac{9\sqrt{3}}{8}$ sq. units