4. Relative to a fixed origin, \(O\), the points \(A\) and \(B\) have position vectors \(\left( \begin{array} { c } 1
5
- 1 \end{array} \right)\) and \(\left( \begin{array} { c } 6
3
- 6 \end{array} \right)\) respectively.
Find, in exact, simplified form,
- the cosine of \(\angle A O B\),
- the area of triangle \(O A B\),
- the shortest distance from \(A\) to the line \(O B\).