Relative to a fixed origin OOO, the point B B\,B has position vector (7i−5j+3k)(7\mathbf{i} - 5\mathbf{j} + 3\mathbf{k})(7i−5j+3k), the point C C\,C has position vector (ai+3j−4k)(a\mathbf{i} + 3\mathbf{j} - 4\mathbf{k})(ai+3j−4k), where a a\,a is a constant and a>0a > 0a>0, and the point D D\,D has position vector (11i−14j+8k)(11\mathbf{i} - 14\mathbf{j} + 8\mathbf{k})(11i−14j+8k). A A\,A is the point such that AB→=BD→\overrightarrow{AB} = \overrightarrow{BD}AB=BD
Find the position vector of AAA.
Given that a=3+25a = 3 + 2\sqrt{5}a=3+25, find the value of ∣AC⃗∣|\vec{AC}|∣AC∣.
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.