Relative to a fixed origin OOO, the point A A\,A has position vector (4i−2j+3k)(4\mathbf{i} - 2\mathbf{j} + 3\mathbf{k})(4i−2j+3k), the point B B\,B has position vector (6i−7j+2k)(6\mathbf{i} - 7\mathbf{j} + 2\mathbf{k})(6i−7j+2k), and the point C C\,C has position vector (2i−5j−k)(2\mathbf{i} - 5\mathbf{j} - \mathbf{k})(2i−5j−k).
Find BC⃗\vec{BC}BC
Show that the quadrilateral OABC OABC\,OABC is a parallelogram, 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.