Let the vertices of the $\Delta \mathrm{ABC}$ are $\mathrm{A}(3,-1,2)$, $\mathrm{B}(1,-1,-3)$ and $\mathrm{C}(4,-3,1)$
Let $\overrightarrow{\mathrm{OA}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}$
$\overrightarrow{\mathrm{OB}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}-3 \hat{\mathrm{k}}$ and
$$
\overrightarrow{\mathrm{OC}}=4 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+\mathrm{k}
$$
Area of $\Delta \mathrm{ABC}=\frac{1}{2}|\overrightarrow{\mathrm{AB}} \times \overrightarrow{\mathrm{AC}}|$
Now, $\overrightarrow{\mathrm{AB}}=\overline{\mathrm{OA}}-\overrightarrow{\mathrm{OB}}=2 \hat{\mathrm{i}}+5 \hat{\mathrm{k}}$
$\overrightarrow{\mathrm{AC}}=\overrightarrow{\mathrm{OA}}-\overrightarrow{\mathrm{OC}}=-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$
$\therefore \quad$ Required Area $=\frac{1}{2}\left\|\begin{array}{|ccc}\hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ 2 & 0 & 5 \\ -1 & 2 & 1\end{array}\right\|$
$=\frac{1}{2}|\hat{i}(-10)-\hat{j}(2+5)+\hat{k}(4)|$
$=\frac{1}{2}|-10 \hat{i}-7 \hat{j}+4 \hat{k}|$
$=\frac{1}{2} \sqrt{100+49+16}=\frac{1}{2} \sqrt{165}$ squnit