Let \( \vec a=\hat i+2\hat j+\hat k \) and \( \vec b=2\hat i+7\hat j+3\hat k \). Let \( L_1:\ \vec r=(-\hat i+2\hat j+\hat k)+\lambda \vec a,\, \lambda\in \mathbb{R} \) and \( L_2:\ \vec r=(\hat j+\hat k)+\mu \vec b,\, \mu\in \mathbb{R} \) be two lines. If the line \( L_3 \) passes through the point of intersection of \( L_1 \) and \( L_2 \), and is parallel to \( \vec a+\vec b \), then \( L_3 \) passes through the point:
