At 08:00 ship X X\,X has position vector (4i+2j)(4\mathbf{i} + 2\mathbf{j})(4i+2j) km and moves with constant velocity (−2i+3j)(-2\mathbf{i} + 3\mathbf{j})(−2i+3j) km h−1\text{h}^{-1}h−1. Another ship Y Y\,Y has position vector (−i−4j)(-\mathbf{i} - 4\mathbf{j})(−i−4j) km and moves with constant velocity (3i+5j)(3\mathbf{i} + 5\mathbf{j})(3i+5j) km h−1\text{h}^{-1}h−1.
Find the relative displacement of ship X X\,X from ship Y Y\,Y after t t\,t hours.
Find the time when X X\,X is due west of YYY.
Find the time, after 08:00, when the ships are exactly 229 \sqrt{229}\,229 km apart.
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.