Relative to a fixed origin OOO, the position vectors of three collinear sensors AAA, BBB, and C C\,C are a\mathbf{a}a, b\mathbf{b}b, and c\mathbf{c}c respectively. The sensor B B\,B is located such that the distance AC AC\,AC is triple the distance ABABAB. Given that B B\,B lies between A A\,A and CCC, show that:
c=3b−2a \mathbf{c} = 3\mathbf{b} - 2\mathbf{a} c=3b−2aProve by contradiction that for any integer nnn, if n2 n^2\,n2 is divisible by 3, then n n\,n is divisible by 3.
Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, matched to the Edexcel A Level Maths (9MA0) 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.
