4. The position of an aeroplane flying in a straight horizontal line at constant speed is plotted on a radar screen. At 2 p.m. the position vector of the aeroplane is \(( 80 \mathbf { i } + 5 \mathbf { j } )\), where \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors directed east and north respectively relative to a fixed origin, \(O\), on the screen. Ten minutes later the position of the aeroplane on the screen is \(( 32 \mathbf { i } + 19 \mathbf { j } )\). Each unit on the screen represents 1 km .

1. Find the position vector of the aeroplane at 2:30 p.m.
2. Find the speed of the aeroplane in \(\mathrm { km } \mathrm { h } ^ { - 1 }\).
3. Find, correct to the nearest degree, the bearing on which the aeroplane is flying.