Let a =2 i +λ_1 j +3 k, b =4 i +(3-λ_2) j +6 k and c =3 i +6 j +(λ_3-1) k be three vectors such that b =2 a and a is perpendicular to c. Then a…

Let $\displaystyle \overrightarrow{\mathrm{a}}=2 \hat{i}+\lambda_1 \hat{j}+3 \hat{k}, \overrightarrow{\mathrm{~b}}=4 \hat{i}+\left(3-\lambda_2\right) \hat{j}+6 \hat{k}$ and $\displaystyle \overrightarrow{\mathrm{c}}=3 \hat{i}+6 \hat{j}+\left(\lambda_3-1\right) \hat{k}$ be three vectors such that $\displaystyle \vec{b}=2 \vec{a}$ and $\displaystyle \vec{a}$ is perpendicular to $\displaystyle \vec{c}$. Then a possible value of $\displaystyle \left(\lambda_1, \lambda_2, \lambda_3\right)$ is :