At 2 p.m. drone P P\,P has position vector (2i+7j)(2\mathbf{i} + 7\mathbf{j})(2i+7j) m and moves with constant velocity (i−2j)(\mathbf{i} - 2\mathbf{j})(i−2j) m s−1\text{s}^{-1}s−1. Another drone Q Q\,Q has position vector (−3i+j)(-3\mathbf{i} + \mathbf{j})(−3i+j) m and moves with constant velocity (5i+2j)(5\mathbf{i} + 2\mathbf{j})(5i+2j) m s−1\text{s}^{-1}s−1.
Find the relative displacement of drone P P\,P from drone Q Q\,Q after t t\,t seconds.
Find the time when P P\,P is due west of QQQ.
Find the time, after 2 p.m., when the drones are exactly 85 \sqrt{85}\,85 m 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.