Relative to a fixed origin OOO, the point A A\,A has position vector (2i+j−k)(2\mathbf{i}+\mathbf{j}-\mathbf{k})(2i+j−k), the point B B\,B has position vector (4i−2j+2k)(4\mathbf{i}-2\mathbf{j}+2\mathbf{k})(4i−2j+2k), and the point C C\,C has position vector (ai+2j−k)(a\mathbf{i}+2\mathbf{j}-\mathbf{k})(ai+2j−k), where a a\,a is a constant and a>0a>0a>0. D D\,D is the point such that AB⃗=BD⃗\vec{AB}=\vec{BD}AB=BD
Find the position vector of DDD.
Given that ∣AC→∣=3|\overrightarrow{AC}|=3∣AC∣=3, find the value of aaa.
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.