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.
309 exam-style questions on Edexcel A Level Maths Vectors, covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics. Each one has a worked solution and a mark scheme showing where the marks go.