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.
168 exam-style questions on AQA A Level Maths 1.13 J: Vectors, 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. Each one has a worked solution and a mark scheme showing where the marks go.