Relative to a fixed origin OOO, the point A A\,A has position vector (4i−2j−5k)(4\mathbf{i} - 2\mathbf{j} - 5\mathbf{k})(4i−2j−5k), AB⃗=2i+3j−4k\vec{AB} = 2\mathbf{i} + 3\mathbf{j} - 4\mathbf{k}AB=2i+3j−4k, and the point C C\,C has position vector (4i+6j−8k)(4\mathbf{i} + 6\mathbf{j} - 8\mathbf{k})(4i+6j−8k).
Find the position vector of BBB
Show that the quadrilateral OABC OABC\,OABC is a trapezium, giving reasons for your answer.
67 exam-style questions on Edexcel A Level Maths 12.3 Solving Geometric Problems. Each one has a worked solution and a mark scheme showing where the marks go.