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.
168 exam-style questions on OCR (MEI) A Level Maths 1.11 Vectors, covering 1.11.1 Language of vectors in two dimensions, 1.11.2 Add, subtract and scale vectors, 1.11.3 Magnitude and direction of a vector, 1.11.4 Position vectors, 1.11.5 Distance between points by position vectors, 1.11.6 Vectors to solve problems, 1.11.7 Language of vectors in three dimensions (A-level only), and 1.11 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.