Relative to a fixed origin OOO, the point A A\,A has position vector (2i−3j+4k)(2\mathbf{i} - 3\mathbf{j} + 4\mathbf{k})(2i−3j+4k), the point B B\,B has position vector (5i−10j+2k)(5\mathbf{i} - 10\mathbf{j} + 2\mathbf{k})(5i−10j+2k), and the point C C\,C has position vector (3i−7j−2k)(3\mathbf{i} - 7\mathbf{j} - 2\mathbf{k})(3i−7j−2k).
Find BC⃗\vec{BC}BC
Show that the quadrilateral OABC OABC\,OABC is a parallelogram, giving reasons for your answer.
Practise AQA A Level Maths 1.13 J: Vectors with exam-style questions for A Level Maths. 122 questions 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, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
