本帖最后由 hbghlyj 于 2020-1-28 10:09 编辑
$\mathbf R^3=\{\vec a=(a_1,a_2,a_3)\mid a_1,a_2,a_3\in\mathbf R\}$,(外积)$\forall \vec a,\vec b \in {{\bf{R}}^3}[\vec a \wedge \vec b = ({a_2}{b_3} - {a_3}{b_2},{a_3}{b_1} - {a_1}{b_3},{a_1}{b_2} - {a_2}{b_1})],$,求所有f:$f:\mathbf R^3\to\mathbf R^3$,使$\forall \vec a,\vec b\in\mathbf R^3:(\vec a\wedge \vec b)\wedge(f(\vec a)\wedge f(\vec b))\parallel f((\vec a\wedge f(\vec b))\wedge(f(\vec a)\wedge \vec b))$ |