1. \hspace{0pt} [In this question the horizontal unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are due east and due north respectively.]

A model boat \(A\) moves on a lake with constant velocity \(( - \mathbf { i } + 6 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). At time \(t = 0 , A\) is at the point with position vector \(( 2 \mathbf { i } - 10 \mathbf { j } ) \mathrm { m }\). Find

1. the speed of \(A\),
2. the direction in which \(A\) is moving, giving your answer as a bearing. At time \(t = 0\), a second boat \(B\) is at the point with position vector \(( - 26 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m }\).
   Given that the velocity of \(B\) is \(( 3 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\),
3. show that \(A\) and \(B\) will collide at a point \(P\) and find the position vector of \(P\). Given instead that \(B\) has speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and moves in the direction of the vector \(( 3 \mathbf { i } + 4 \mathbf { j } )\),
4. find the distance of \(B\) from \(P\) when \(t = 7 \mathrm {~s}\).