3d Geometry

Let \(L_1: \vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+\lambda(\hat{i}-\hat{j}+2 \hat{k}), \lambda \in \mathbb{R}\),

\(L_2: \vec{r}=(\hat{j}-\hat{k})+\mu(3 \hat{i}+\hat{j}+p \hat{k}), \mu \in \mathbb{R} \text {, and } L_3: \vec{r}=\delta(\ell \hat{i}+m \hat{j}+n \hat{k}), \delta \in \mathbb{R}\)

be three lines such that \(L_1\) is perpendicular to \(L_2\) and \(L_3\) is perpendicular to both \(L_1\) and \(L_2\). Then, the point which lies on \(L_3\) is