In this question the origin is taken to be at a harbour and the unit vectors i and j to have lengths of 1km in the directions E and N.

A cargo vessel leaves the harbour and its position vector t hours later is given by - r1 = 12ti + 16tj

A fishing boat is trawling nearby and its position at a time t is given by - r2 = (10 - 3t)i + (8+4t)j

Questions: 1) How far apart are the two boats when the cargo vessel leaves harbour?

2) How fast is each boat traveling?

Answers: 1) 12.8km

2) 20 km per hour a 5 km per hour

Can you guys explain to me how they got these answers? Your help is much appreciated