Relative to a fixed origin OOO, a drone P P\,P has position vector (3i+2j−k)(3\mathbf{i} + 2\mathbf{j} - \mathbf{k})(3i+2j−k), a drone Q Q\,Q has position vector (7i+5j+3k)(7\mathbf{i} + 5\mathbf{j} + 3\mathbf{k})(7i+5j+3k), and a drone R R\,R has position vector (4i+3j+4k)(4\mathbf{i} + 3\mathbf{j} + 4\mathbf{k})(4i+3j+4k).
Find the vector QR⃗\vec{QR}QR.
Show that the quadrilateral OPQR OPQR\,OPQR 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.