Two forces F1\mathbf{F}_1F1 and F2\mathbf{F}_2F2 act on a particle. F1=6i−3j+k\mathbf{F}_1 = 6\mathbf{i} - 3\mathbf{j} + \mathbf{k}F1=6i−3j+k and F2=xi+yj+zk\mathbf{F}_2 = x\mathbf{i} + y\mathbf{j} + z\mathbf{k}F2=xi+yj+zk.
The total resultant force acting on the particle is 10i+4j−5k10\mathbf{i} + 4\mathbf{j} - 5\mathbf{k}10i+4j−5k. Calculate the values of the constants xxx, yyy, and zzz.
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.