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 AB→=BD→\overrightarrow{AB} = \overrightarrow{BD}AB=BD.
Find the position vector of DDD.
Given that ∣AC⃗∣=7|\vec{AC}| = 7∣AC∣=7, find the value of aaa.
95 exam-style questions on WJEC A Level Maths 4.11.1 Vectors (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.