A deep-space exploration craft, C1C_1C1, is traveling with a constant velocity v1=(12i−16j+10k) km s−1\mathbf{v}_1 = (12\mathbf{i} - 16\mathbf{j} + 10\mathbf{k}) \text{ km s}^{-1}v1=(12i−16j+10k) km s−1. A second craft, C2C_2C2, maintains a constant velocity v2=(−18i+kj−15k) km s−1\mathbf{v}_2 = (-18\mathbf{i} + k\mathbf{j} - 15\mathbf{k}) \text{ km s}^{-1}v2=(−18i+kj−15k) km s−1. Given that the motion of C2C_2C2 is parallel to the motion of C1C_1C1, determine the value of the scalar constant 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.