Let $\overrightarrow{\mathrm{a}}=2\overrightarrow{\mathrm{i}}+{\mathrm{\lambda }}_1\overrightarrow{\mathrm{j}}+3\overrightarrow{\mathrm{k}}, \overrightarrow{\mathrm{b}}=4\overrightarrow{\mathrm{i}}+(3-{\mathrm{\lambda }}_2)\overrightarrow{\mathrm{j}}+6\overrightarrow{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=3\hat{\mathrm{i}}+6\hat{\mathrm{j}}+({\mathrm{\lambda }}_3-1)\hat{\mathrm{k}}$ be three vectors such that $\overrightarrow{\mathrm{b}}=2\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{a}}$ is perpendicular to $\overrightarrow{\mathrm{c}}$ Then a possible value of $\left({\mathrm{\lambda }}_1, {\mathrm{\lambda }}_2,{\mathrm{\lambda }}_3\right)$ is :

$$\begin{gathered} \overline{\mathrm{b}}=2\overline{\mathrm{a}} \Rightarrow 4\mathrm{i}+(3-\mathrm{\lambda }2)\mathrm{j}+6\mathrm{k}=4\mathrm{i}+2{\mathrm{\lambda }}_1\mathrm{j}+6\mathrm{k} \\ 2{\mathrm{\lambda }}_1=3-{\mathrm{\lambda }}_2 \Rightarrow 2{\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2=3 -\left(1\right) \\ \overline{\mathrm{a}}.\overline{\mathrm{c}}=0 \Rightarrow 6+6{\mathrm{\lambda }}_1+3{\mathrm{\lambda }}_2-3=0 \\ 6{\mathrm{\lambda }}_1+3{\mathrm{\lambda }}_3+3=0 \\ 2{\mathrm{\lambda }}_1+{\mathrm{\lambda }}_3+1=0 -\left(2\right) \\ \therefore \mathrm{option} \mathrm{vertification} \end{gathered}$$