Three Dimensional Geometry: JEE Main 2025 Mathematics question

Let $\overrightarrow{\mathrm{a}}=\hat{\imath}+2\hat{\jmath}+\hat{k}$ and $\overrightarrow{\mathrm{b}}=2\hat{\imath}+7\hat{\jmath}+3\hat{k}$. Let $\mathrm{L}_1: \overrightarrow{\mathrm{r}}=(-\hat{\imath}+2\hat{\jmath}+\hat{k})+\lambda \overrightarrow{\mathrm{a}}, \lambda \in \mathbf{R}$ and $\mathrm{L}_2: \overrightarrow{\mathrm{r}}=(\hat{\jmath}+\hat{k})+\mu \overrightarrow{\mathrm{b}}, \mu \in \mathbf{R}$ be two lines. If the line $\mathrm{L}_3$ passes through the point of intersection of $\mathrm{L}_1$ and $\mathrm{L}_2$, and is parallel to $\vec{a}+\vec{b}$, then $\mathrm{L}_3$ passes through the point: