Consider the vectors u=−2i+5j+8k\mathbf{u} = -2\mathbf{i} + 5\mathbf{j} + 8\mathbf{k}u=−2i+5j+8k and v=xi+yj+zk\mathbf{v} = x\mathbf{i} + y\mathbf{j} + z\mathbf{k}v=xi+yj+zk.
Given that the sum of vectors u\mathbf{u}u and v\mathbf{v}v is −7i−j+3k-7\mathbf{i} - \mathbf{j} + 3\mathbf{k}−7i−j+3k, determine the values of xxx, yyy, and zzz.
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.