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Slope of a Line

Construct set...

Question

Construct sets of $4$ and $5$ vectors that have $8$ and $10$ maximal subsets respectively

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Solution

For $n = 4$ , consider a convex quadrilateral ABCD in which $A B = B C = A C = B D$ and $A D = D C$ , and take the vectors $\to A B, \to B C, \to C D, \to D A$ . For $n = 5$ , take the vectors $\to A B, \to B C, \to C D, \to D E, \to E A$ for any regular pentagon ABCDE.

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