[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.
The motion of the boat is modelled as that of a particle moving in a straight line at constant speed.
The boat is moving on a bearing of 225∘ 225^\circ\,225∘ at a speed of 32 km h−13\sqrt{2}\text{ km h}^{-1}32 km h−1.
Calculate the distance travelled by the boat between 08:00 and 10:20.
Calculate the position of the boat at 10:20 relative to OOO.
284 exam-style questions on Edexcel A Level Maths Vectors, covering 11.1 Vectors, 11.2 Representing Vectors, 11.3 Magnitude and Direction, 11.4 Position Vectors, 11.5 Solving Geometric Problems, and 11.6 Modelling with Vectors. Each one has a worked solution and a mark scheme showing where the marks go.