8 The line \(l\) has equation \(\mathbf { r } = \left( \begin{array} { r } 1
2
- 1 \end{array} \right) + \lambda \left( \begin{array} { l } 2
1
3 \end{array} \right)\). The plane \(p\) has equation \(\mathbf { r } \cdot \left( \begin{array} { r } 2
- 1
- 1 \end{array} \right) = 6\).
- Show that \(l\) is parallel to \(p\).
- A line \(m\) lies in the plane \(p\) and is perpendicular to \(l\). The line \(m\) passes through the point with coordinates (5, 3, 1). Find a vector equation for \(m\).