Ask Uncle Colin: A STEP vectors problem | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.

Dear Uncle Colin,

I’m struggling with this STEP question. The first two parts are fine — equality holds when there is some constant $k$ for which $a = kx$, $b = ky$ and $c=kz$, and part (i) follows directly from the original inequality.

I can get an answer to part (ii) — $\colvecthree {p}{q}{r} = \colvecthree{24}{6}{1}$ — but that’s from luck,…

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