6. [In this question, the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are due east and due north respectively.] A particle \(P\) is moving with constant velocity \(( - 5 \mathbf { i } + 8 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Find

1. the speed of \(P\),
2. the direction of motion of \(P\), giving your answer as a bearing. At time \(t = 0 , P\) is at the point \(A\) with position vector ( \(7 \mathbf { i } - 10 \mathbf { j }\) ) m relative to a fixed origin \(O\). When \(t = 3 \mathrm {~s}\), the velocity of \(P\) changes and it moves with velocity \(( u \mathbf { i } + v \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\), where \(u\) and \(v\) are constants. After a further 4 s , it passes through \(O\) and continues to move with velocity ( \(u \mathbf { i } + v \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
3. Find the values of \(u\) and \(v\).
4. Find the total time taken for \(P\) to move from \(A\) to a position which is due south of A.