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Show the fact for any vectors a,b in Euclidean space

Source: IMO LongList 1979 - P20

September 15, 2010
vectortrigonometrygeometrygeometric inequalityeuclidean geometryIMO ShortlistIMO Longlist

Problem Statement

Show that for any vectors a,ba, b in Euclidean space, ∣a×b∣3≤338∣a∣2∣b∣2∣a−b∣2|a \times b|^3 \leq \frac{3 \sqrt 3}{8} |a|^2 |b|^2 |a-b|^2 Remark. Here ×\times denotes the vector product.
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