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.
Practise AQA A Level Maths 1.13 J: Vectors with exam-style questions for A Level Maths. 122 questions covering 1.13.1 Vectors in two and three dimensions, 1.13.2 Magnitude and direction of a vector, 1.13.3 Vector arithmetic, 1.13.4 Position vectors, and 1.13.5 Vectors to solve problems, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
