Question 10
(FIN 3) Show that for any vectors $a,b$ in Euclidean space,
$$|a\times b|^3\le\frac{3\sqrt3}{8}|a|^2|b|^2|a-b|^2.$$
Remark. Here $\times$ denotes the vector product.
$$|a\times b|^3\le\frac{3\sqrt3}{8}|a|^2|b|^2|a-b|^2.$$
Remark. Here $\times$ denotes the vector product.