Ans: (C)
Hint : Let d.c. of line is \((\mathrm{k}, \mathrm{k}, \mathrm{k})\)
$$
\begin{aligned}
&\Rightarrow 3 \mathrm{k}^{2}=1 \Rightarrow \mathrm{k}=\frac{1}{\sqrt{3}} \\
&\Rightarrow \text { d.c. of line is }\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right)
\end{aligned}
$$
Equation of a line passing through point \(p\) is
$$
\begin{aligned}
&\frac{x-2}{\frac{1}{\sqrt{3}}}=\frac{y+1}{\frac{1}{\sqrt{3}}}=\frac{z-2}{\frac{1}{\sqrt{3}}}=k \\
&\Rightarrow x=k+2, y=k-1, z=k+2 \\
&\therefore 2(k+2)+(k-1)+(k+2)=9 \\
&4 k=4 \Rightarrow k=1 \\
&\therefore \text { Point } Q \text { is }(3,0,3) \\
&P Q=\sqrt{1^{2}+1^{2}+1^{2}}=\sqrt{3} \text { units. }
\end{aligned}
$$
