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.
Practise AQA A Level Maths 1.13 J: Vectors with exam-style questions for A Level Maths. 122 questions covering 1.13.1 Vectors in two and three dimensions, 1.13.2 Magnitude and direction of a vector, 1.13.3 Vector arithmetic, 1.13.4 Position vectors, and 1.13.5 Vectors to solve problems, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
