Let L_1: r =( i - j +2 k )+λ( i - j +2 k ), λ ∈ R, L_2: r =( j - k )+μ(3 i + j +p k ), μ ∈ R, and L_3: r =δ(ℓ i +m j +n k ), δ ∈ R be three lines…

Let $\displaystyle L_1: \vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+\lambda(\hat{i}-\hat{j}+2 \hat{k}), \lambda \in \mathbb{R}$, $\displaystyle L_2: \vec{r}=(\hat{j}-\hat{k})+\mu(3 \hat{i}+\hat{j}+p \hat{k}), \mu \in \mathbb{R}$, and $\displaystyle L_3: \vec{r}=\delta(\ell \hat{i}+m \hat{j}+n \hat{k}), \delta \in \mathbb{R}$ be three lines such that $\displaystyle L_1$ is perpendicular to $\displaystyle L_2$ and $\displaystyle L_3$ is perpendicular to both $\displaystyle L_1$ and $\displaystyle L_2$. Then, the point which lies on $\displaystyle L_3$ is