A particle is held in equilibrium by three horizontal forces. Two of the forces are (8i+6j)(8\mathbf{i} + 6\mathbf{j})(8i+6j) N and (−3i+4j)(-3\mathbf{i} + 4\mathbf{j})(−3i+4j) N, where i\mathbf{i}i and j\mathbf{j}j are perpendicular unit vectors.
The third force is F\mathbf{F}F N.
Find F\mathbf{F}F in component form.
Find the magnitude of F\mathbf{F}F.
87 exam-style questions on OCR (MEI) A Level Maths 3.4 Forces, covering 3.4.1 Language relating to forces, 3.4.2 Acceleration due to gravity, 3.4.3 Identify forces and draw force diagrams, 3.4.4 Resultant of concurrent forces, 3.4.5 Equilibrium of a particle, 3.4.6 Resolve a force into components (A-level only), 3.4.7 Equilibrium condition for resultant zero (A-level only), 3.4.8 Forces in equilibrium sum to zero (A-level only), 3.4.9 Equations for a particle in equilibrium (A-level only), 3.4.10 Frictional force and normal contact force (A-level only), 3.4.11 Model friction with F ≤ μR (A-level only), and 3.4.12 Apply Newton's Laws to friction problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.