- Relative to a fixed origin \(O\),
- \(A\) is the point with position vector \(12 \mathbf { i }\)
- \(B\) is the point with position vector \(16 \mathbf { j }\)
- \(C\) is the point with position vector \(( 50 \mathbf { i } + 136 \mathbf { j } )\)
- \(D\) is the point with position vector \(( 22 \mathbf { i } + 24 \mathbf { j } )\)
- Show that \(A D\) is parallel to \(B C\).
Points \(A , B , C\) and \(D\) are used to model the vertices of a running track in the shape of a quadrilateral.
Runners complete one lap by running along all four sides of the track.
The lengths of the sides are measured in metres.
Given that a particular runner takes exactly 5 minutes to complete 2 laps,
calculate the average speed of this runner, giving the answer in kilometres per hour.