The points AAA, B B\,B and C C\,C have position vectors
a=2i+3j−k\mathbf{a} = 2\mathbf{i} + 3\mathbf{j} - \mathbf{k}a=2i+3j−k, b=5i−j+2k\mathbf{b} = 5\mathbf{i} - \mathbf{j} + 2\mathbf{k}b=5i−j+2k, c=μi+11j+νk\mathbf{c} = \mu\mathbf{i} + 11\mathbf{j} + \nu\mathbf{k}c=μi+11j+νk
where μ \mu\,μ and ν \nu\,ν are constants.
Find AB⃗\vec{AB}AB and ∣AB⃗∣\left|\vec{AB}\right|AB, giving the magnitude in exact form.
Given that AC⃗\vec{AC}AC is parallel to AB⃗\vec{AB}AB, find the value of μ \mu\,μ and the value of ν\nuν.
Hence write down the ratio AB:ACAB : ACAB:AC.
168 exam-style questions on OCR (MEI) A Level Maths 1.11 Vectors, covering 1.11.1 Language of vectors in two dimensions, 1.11.2 Add, subtract and scale vectors, 1.11.3 Magnitude and direction of a vector, 1.11.4 Position vectors, 1.11.5 Distance between points by position vectors, 1.11.6 Vectors to solve problems, 1.11.7 Language of vectors in three dimensions (A-level only), and 1.11 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.