Three forces act on a particle:
F1=(5i−2j+3k)\mathbf{F}_1 = (5\mathbf{i} - 2\mathbf{j} + 3\mathbf{k})F1=(5i−2j+3k) N, F2=(−3i+7j−k)\mathbf{F}_2 = (-3\mathbf{i} + 7\mathbf{j} - \mathbf{k})F2=(−3i+7j−k) N, F3=(ai+bj−2k)\mathbf{F}_3 = (a\mathbf{i} + b\mathbf{j} - 2\mathbf{k})F3=(ai+bj−2k) N
where a a\,a and b b\,b are constants.
Given that the particle is in equilibrium, find the value of a a\,a and the value of bbb.
The force F3\mathbf{F}_3F3 is now removed. Find the magnitude of the resultant of F1\mathbf{F}_1F1 and F2\mathbf{F}_2F2, giving your answer in newtons to three significant figures.
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.