Let a = i +2 j + k and b =2 i +7 j +3 k. Let L_1: r =(- i +2 j + k )+λ a, λ ∈ R and L_2: r =( j + k )+μ b, μ ∈ R be two lines. If the line L_3 passes…

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