Vector Algebra: JEE Main 2022 Mathematics question

Let $\overrightarrow{\mathrm{a}}=3 \hat{i}+\hat{j}$ and $\overrightarrow{\mathrm{b}}=\hat{i}+2 \hat{j}+\hat{k}$. Let $\overrightarrow{\mathrm{c}}$ be a vector satisfying $\overrightarrow{\mathrm{a}} \times(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}})=\overrightarrow{\mathrm{b}}+\lambda \overrightarrow{\mathrm{c}}$. If $\overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{c}}$ are non-parallel, then the value of $\lambda$ is :