Let $L_1:\ \vec r=(\hat i-\hat j+2\hat k)+\lambda(\hat i-\hat j+2\hat k),\ \lambda\in\mathbb R,$ $L_2:\ \vec r=(\hat j-\hat k)+\mu(3\hat i+\hat j+p\hat k),\ \mu\in\mathbb R,$ 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: