Relative to a fixed origin OOO, the point A A\,A has position vector (4i−j+3k)(4\mathbf{i} - \mathbf{j} + 3\mathbf{k})(4i−j+3k), the point B B\,B has position vector (2i+3j−k)(2\mathbf{i} + 3\mathbf{j} - \mathbf{k})(2i+3j−k), and the point C C\,C has position vector (ai+2j+5k)(a\mathbf{i} + 2\mathbf{j} + 5\mathbf{k})(ai+2j+5k), 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 ∣AC⃗∣=7|\vec{AC}| = 7∣AC∣=7, find the value of aaa.
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.
