Two forces (5i−3j)(5\mathbf{i} - 3\mathbf{j})(5i−3j) N and (−2i+7j)(-2\mathbf{i} + 7\mathbf{j})(−2i+7j) N act on a particle AAA.
A third force F\mathbf{F}F also acts on AAA, and A A\,A is in equilibrium.
Find F\mathbf{F}F, giving your answer in terms of i\mathbf{i}i and j\mathbf{j}j.
Find the magnitude of F\mathbf{F}F.
139 exam-style questions on AQA A Level Maths 3.3 R: Forces and Newton's laws, covering 3.3.1 Concept of a force and Newton's first law, 3.3.2 Newton's second law, 3.3.3 Weight and motion under gravity, 3.3.4 Newton's third law and equilibrium, 3.3.5 Addition of forces and resultants (A-level only), and 3.3.6 Friction (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.