6. [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors due east and due north respectively. Position vectors are given with respect to a fixed origin \(O\).] A ship \(S\) is moving with constant velocity \(( 3 \mathbf { i } + 3 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\). At time \(t = 0\), the position vector of \(S\) is \(( - 4 \mathbf { i } + 2 \mathbf { j } ) \mathrm { km }\).

1. Find the position vector of \(S\) at time \(t\) hours. A ship \(T\) is moving with constant velocity \(( - 2 \mathbf { i } + n \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\). At time \(t = 0\), the position vector of \(T\) is \(( 6 \mathbf { i } + \mathbf { j } ) \mathrm { km }\). The two ships meet at the point \(P\).
2. Find the value of \(n\).
3. Find the distance \(O P\).