Relative to a fixed origin OOO, the point A A\,A has position vector (5i+2j−3k)(5\mathbf{i} + 2\mathbf{j} - 3\mathbf{k})(5i+2j−3k), the point B B\,B has position vector (8i+3j−6k)(8\mathbf{i} + 3\mathbf{j} - 6\mathbf{k})(8i+3j−6k), and the point C C\,C has position vector (−6i−2j+6k)(-6\mathbf{i} - 2\mathbf{j} + 6\mathbf{k})(−6i−2j+6k).
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.