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 to 1 decimal place.
Calculate the speed of the boat, giving your answer in km h−1^{-1}−1 to 3 significant figures.
197 exam-style questions on OCR A Level Maths 1.10 Vectors, covering 1.10.1 Vectors in two dimensions, 1.10.2 Vectors in three dimensions (A-level only), 1.10.3 Magnitude and direction of vectors, 1.10.4 Basic operations on vectors, 1.10.5 Position vectors, 1.10.6 Distance between points, 1.10.7 Problem solving using vectors, 1.10.8 Vectors in kinematics, and 1.10 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.