Relative to a fixed origin OOO, the point A A\,A has position vector (3i−4j+5k)(3\mathbf{i} - 4\mathbf{j} + 5\mathbf{k})(3i−4j+5k), the point B B\,B has position vector (7i−10j+2k)(7\mathbf{i} - 10\mathbf{j} + 2\mathbf{k})(7i−10j+2k), and the point C C\,C has position vector (4i−6j−3k)(4\mathbf{i} - 6\mathbf{j} - 3\mathbf{k})(4i−6j−3k).
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.