IMO Shortlist 1979 problem 10
Dodao/la:
arhiva2. travnja 2012. Show that for any vectors
![a, b](/media/m/a/2/b/a2bdbf048e2daac0a021a1d79f6fb9bf.png)
in Euclidean space,
![|a \times b|^3 \leq \frac{3 \sqrt 3}{8} |a|^2 |b|^2 |a-b|^2](/media/m/3/1/0/31036edf7e286592c061131407902477.png)
Remark. Here
![\times](/media/m/d/2/1/d21c81775b905b7490d1685dd27285e5.png)
denotes the vector product.
%V0
Show that for any vectors $a, b$ in Euclidean space,
$$|a \times b|^3 \leq \frac{3 \sqrt 3}{8} |a|^2 |b|^2 |a-b|^2$$
Remark. Here $\times$ denotes the vector product.
Izvor: Međunarodna matematička olimpijada, shortlist 1979