6. The points \(A\) and \(B\) have position vectors \(( 30 \mathbf { i } - 60 \mathbf { j } ) \mathrm { m }\) and \(( - 20 \mathbf { i } + 60 \mathbf { j } ) \mathrm { m }\) respectively relative to an origin \(O\), where \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular unit vectors. A cyclist, Chris, starts at \(A\) and cycles towards \(B\) with constant speed \(2.6 \mathrm {~ms} ^ { - 1 }\). Another cyclist, Doug, starts at \(O\) and cycles towards \(B\) with constant speed \(k \sqrt { } 10 \mathrm {~ms} ^ { - 1 }\).

1. Show that Chris's velocity vector is \(( - \mathbf { i } + 2 \cdot 4 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\).
2. Find Doug's velocity vector in the form \(k ( a \mathbf { i } + b \mathbf { j } ) \mathrm { ms } ^ { - 1 }\). Given that Chris and Doug arrive at \(B\) at the same time,
3. find the value of \(k\).