The plane passing through the point

Let $\overrightarrow{\mathrm{n}}$ be the normal vector to the plane passing through $(4,-1,2)$ and parallel to the lines $\mathrm{L}_{1} \& \mathrm{~L}_{2}$

then $\overrightarrow{\mathrm{n}}=\left|\begin{array}{ccc}\hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ 3 & -1 & 2 \\ 1 & 2 & 3\end{array}\right|$

$\therefore \overrightarrow{\mathrm{n}}=-7 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}$

$\therefore$ Equation of plane is

$-1(x-4)-1(y+1)+1(z-2)=0$

$\therefore x+y-z-1=0$

Now check options