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.
Practise Edexcel A Level Maths 12.3 Solving Geometric Problems with exam-style questions for A Level Maths. 55 questions, matched to the Edexcel A Level Maths (9MA0) 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.
