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.
168 exam-style questions on OCR (MEI) A Level Maths 1.11 Vectors, covering 1.11.1 Language of vectors in two dimensions, 1.11.2 Add, subtract and scale vectors, 1.11.3 Magnitude and direction of a vector, 1.11.4 Position vectors, 1.11.5 Distance between points by position vectors, 1.11.6 Vectors to solve problems, 1.11.7 Language of vectors in three dimensions (A-level only), and 1.11 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.