Relative to a fixed origin OOO, the point A A\,A has position vector (2i−j+3k)(2\mathbf{i} - \mathbf{j} + 3\mathbf{k})(2i−j+3k), the point B B\,B has position vector (6i+4j−2k)(6\mathbf{i} + 4\mathbf{j} - 2\mathbf{k})(6i+4j−2k), and the point C C\,C has position vector (ai−4j+k)(a\mathbf{i} - 4\mathbf{j} + \mathbf{k})(ai−4j+k), 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 ∣AC→∣=6|\overrightarrow{AC}| = 6∣AC∣=6, 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.