1.1 Proof by Contradiction

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Relative to a fixed origin $O$ , the position vectors of three collinear sensors $A$ , $B$ , and $C\,$ are $a\mathbf{a}$ , $b\mathbf{b}$ , and $c\mathbf{c}$ respectively. The sensor $B\,$ is located such that the distance $AC\,$ is triple the distance $A B$ . Given that $B\,$ lies between $A\,$ and $C$ , show that: $c=3b−2a\mathbf{c} = 3\mathbf{b} - 2\mathbf{a}$

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ii.

Prove by contradiction that for any integer $n$ , if $n^2\,$ is divisible by 3, then $n\,$ is divisible by 3.

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1.1 Proof by Contradiction Questions

Practise Edexcel A Level Maths 1.1 Proof by Contradiction with exam-style questions for A Level Maths. 100 questions, 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.