5 The line through points \(A ( 8 , - 7 , - 2 )\) and \(B ( 11 , - 9,0 )\) is denoted by \(L _ { 1 }\).
- Find a vector equation for \(L _ { 1 }\).
- Determine whether the point \(( 26 , - 19 , - 14 )\) lies on \(L _ { 1 }\).
The line \(L _ { 2 }\) passes through the origin, \(O\), and intersects \(L _ { 1 }\) at the point \(C\). The lines \(L _ { 1 }\) and \(L _ { 2 }\) are perpendicular.
- By using the fact that \(C\) lies on \(L _ { 1 }\), find a vector equation for \(L _ { 2 }\).
- Hence find the shortest distance from \(O\) to \(L _ { 1 }\).