MathDB

10

Part of 1979 IMO Shortlist

Problems(1)

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

Source: IMO LongList 1979 - P20

9/15/2010
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.
vectortrigonometrygeometrygeometric inequalityeuclidean geometryIMO ShortlistIMO Longlist