Browsing category vectors

Proving three points lie on a straight line (GCSE vectors)

If you ever study GCSE vectors questions, you'll spot a pattern: there's normally a (relatively) straightforward first part which involves writing down a few vectors, and then something like "show that points $O$, $X$ and $Y$ lie on a straight line." Pretty much every student I've ever worked with on

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Dealing with M1 vectors

OK, so you've got to grips with the SUVAT equations, you're on top of resolving forces, you understand that $F=ma$ and you have M1 under control... only for them to start throwing $\bi$s and $\bj$s around. Who ordered those? Maybe you have a vague recollection of vectors from GCSE -

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Why is the dot product the way it is?

(Thanks to Barney Maunder-Taylor for teasing me with this one.) This question interests me for two reasons: Firstly, it's a neat proof in its own right, and I'll start by giving a little sketch of it. Secondly, though, even after Barney gave me the crux of the proof, it still

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