Let \( L_{1}:\ \vec{r} = (\hat{\imath}-\hat{\jmath}+2\hat{k}) + \lambda(\hat{\imath}-\hat{\jmath}+2\hat{k}),\ \lambda \in \mathbb{R}; \ L_{2}:\ \vec{r} = (j-\hat{k}\,) + \mu(3\hat{\imath}+\hat{\jmath}+p\hat{k}),\ \mu \in \mathbb{R}; \) and \( L_{3}:\ \vec{r} = \delta(\hat{\imath}+m\hat{\jmath}+n\hat{k}),\ \delta \in \mathbb{R} \) 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:
