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), the point B B\,B has position vector (6i+j−9k)(6\mathbf{i} + \mathbf{j} - 9\mathbf{k})(6i+j−9k), 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 AB⃗\vec{AB}AB.
Show that the quadrilateral OABC OABC\,OABC is a trapezium, 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.