10 With respect to the origin \(O\), the position vectors of the points \(A\) and \(B\) are given by \(\overrightarrow { O A } = \left( \begin{array} { r } 1
2
- 1 \end{array} \right)\) and \(\overrightarrow { O B } = \left( \begin{array} { l } 0
3
1 \end{array} \right)\).
- Find a vector equation for the line \(l\) through \(A\) and \(B\).
- The point \(C\) lies on \(l\) and is such that \(\overrightarrow { A C } = 3 \overrightarrow { A B }\).
Find the position vector of \(C\).
- Find the possible position vectors of the point \(P\) on \(l\) such that \(O P = \sqrt { 14 }\).