Relative to a fixed origin OOO, the point A A\,A has position vector (2i+5j+6k)(2\mathbf{i} + 5\mathbf{j} + 6\mathbf{k})(2i+5j+6k), the point B B\,B has position vector (i+9j+k)(\mathbf{i} + 9\mathbf{j} + \mathbf{k})(i+9j+k), and the point C C\,C has position vector (−i+4j−5k)(-\mathbf{i} + 4\mathbf{j} - 5\mathbf{k})(−i+4j−5k).
Find BC⃗\vec{BC}BC
Show that the quadrilateral OABC OABC\,OABC is a parallelogram, giving reasons for your answer.
309 exam-style questions on Edexcel A Level Maths Vectors, covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics. Each one has a worked solution and a mark scheme showing where the marks go.