In a particle physics experiment, relative to a fixed origin OOO, particle L L\,L is at position (−i+4j+2k)(- \mathbf{i} + 4\mathbf{j} + 2\mathbf{k})(−i+4j+2k), particle M M\,M is at (2i+j+8k)(2\mathbf{i} + \mathbf{j} + 8\mathbf{k})(2i+j+8k), and particle N N\,N is at (3i−3j+6k)(3\mathbf{i} - 3\mathbf{j} + 6\mathbf{k})(3i−3j+6k).
Find the vector MN⃗\vec{MN}MN.
Show that the quadrilateral OLMN OLMN\,OLMN is a parallelogram, giving reasons for your answer.
109 exam-style questions on Edexcel A Level Maths Vectors, covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics. Each one has a worked solution and a mark scheme showing where the marks go.