Relative to a fixed origin OOO, the vertex D D\,D of a triangular structure has position vector (4i−j+5k)(4\mathbf{i} - \mathbf{j} + 5\mathbf{k})(4i−j+5k), vertex E E\,E has position vector (5i+2j+9k)(5\mathbf{i} + 2\mathbf{j} + 9\mathbf{k})(5i+2j+9k), and vertex F F\,F has position vector (i+3j+4k)(\mathbf{i} + 3\mathbf{j} + 4\mathbf{k})(i+3j+4k).
Find the vector EF⃗\vec{EF}EF.
Show that the quadrilateral ODEF ODEF\,ODEF is a parallelogram, 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.