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.
197 exam-style questions on OCR A Level Maths 1.10 Vectors, covering 1.10.1 Vectors in two dimensions, 1.10.2 Vectors in three dimensions (A-level only), 1.10.3 Magnitude and direction of vectors, 1.10.4 Basic operations on vectors, 1.10.5 Position vectors, 1.10.6 Distance between points, 1.10.7 Problem solving using vectors, 1.10.8 Vectors in kinematics, and 1.10 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.