The points AAA, B B\,B and C C\,C have position vectors
a=i+2j−k\mathbf{a} = \mathbf{i} + 2\mathbf{j} - \mathbf{k}a=i+2j−k, b=4i−j+5k\mathbf{b} = 4\mathbf{i} - \mathbf{j} + 5\mathbf{k}b=4i−j+5k, c=10i−7j+17k\mathbf{c} = 10\mathbf{i} - 7\mathbf{j} + 17\mathbf{k}c=10i−7j+17k
Show that AAA, B B\,B and C C\,C are collinear.
Find the ratio AB:BCAB : BCAB:BC.
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.