A toy boat P P\,P moves across a pond with constant velocity. Initially P P\,P is at the point A A\,A with position vector (−2i+7j) m(-2\mathbf{i} + 7\mathbf{j}) \text{ m}(−2i+7j) m. At time t=2t = 2t=2 seconds, P P\,P is at the point B B\,B with position vector (8i−17j) m(8\mathbf{i} - 17\mathbf{j}) \text{ m}(8i−17j) m.
Find the velocity of PPP.
When t=3t = 3t=3 P P\,P is at the point CCC. Find the distance ACACAC.
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.