[In this question the unit vectors i\mathbf{i}i and j\mathbf{j}j are due east and due north respectively.]
A coastguard station O O\,O monitors the movements of a small boat.
At 08:00 the boat is at the point (3i−4j)(3\mathbf{i} - 4\mathbf{j})(3i−4j) km relative to OOO.
At 10:20 the boat is at the point (−2i−7j)(-2\mathbf{i} - 7\mathbf{j})(−2i−7j) km relative to OOO.
The motion of the boat is modelled as that of a particle moving in a straight line at constant speed.
Calculate the bearing on which the boat is moving, giving your answer in degrees to one decimal place.
Calculate the speed of the boat, giving your answer in km h−1\text{km h}^{-1}km h−1
Practise AQA A Level Maths 1.13 J: Vectors with exam-style questions for A Level Maths. 122 questions covering 1.13.1 Vectors in two and three dimensions, 1.13.2 Magnitude and direction of a vector, 1.13.3 Vector arithmetic, 1.13.4 Position vectors, and 1.13.5 Vectors to solve problems, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
