Two drones, A A\,A and BBB, are performing a synchronized maneuver with constant velocity vectors. The velocity of drone A A\,A is vA=(15i−25j+10k) m s−1\mathbf{v}_A = (15\mathbf{i} - 25\mathbf{j} + 10\mathbf{k}) \text{ m s}^{-1}vA=(15i−25j+10k) m s−1 and the velocity of drone B B\,B is vB=(ki+10j−4k) m s−1\mathbf{v}_B = (k\mathbf{i} + 10\mathbf{j} - 4\mathbf{k}) \text{ m s}^{-1}vB=(ki+10j−4k) m s−1, where k k\,k is a constant. Given that the direction of motion of drone B B\,B is parallel to the direction of motion of drone AAA, determine the value of kkk.
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.