Relative to a fixed origin OOO, the point D D\,D has position vector (−2i+4j+k)(-2\mathbf{i} + 4\mathbf{j} + \mathbf{k})(−2i+4j+k), the point E E\,E has position vector (−3i+6j−3k)(-3\mathbf{i} + 6\mathbf{j} - 3\mathbf{k})(−3i+6j−3k), and the point F F\,F has position vector (4i−8j+16k)(4\mathbf{i} - 8\mathbf{j} + 16\mathbf{k})(4i−8j+16k).
Find DE⃗\vec{DE}DE
Show that the quadrilateral ODEF ODEF\,ODEF is a trapezium, 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.
