记$max\left\{x,y\right\}=\left\{\begin{array}{l}x,x\ge y\\ y,x<y\end{array}\right.$，$min\left\{x,y\right\}=\left\{\begin{array}{l}x,x\ge y\\ y,x<y\end{array}\right.$，设$\stackrel{\rightharpoonup }{a},\stackrel{\rightharpoonup }{b}$为平面向量，则

$min\left\{\left|a+b\right|,\left|a-b\right|\right\}\le min\left\{\left|a\right|,\left|b\right|\right\}$ $min\left\{\left|a+b\right|,\left|a-b\right|\right\}\ge min\left\{\left|a\right|,\left|b\right|\right\}$ $min\left\{{\left|a+b\right|}^2,{\left|a-b\right|}^2\right\}\ge {\left|a\right|}^2+{\left|b\right|}^2$ $min\left\{{\left|a+b\right|}^2,{\left|a-b\right|}^2\right\}\le {\left|a\right|}^2+{\left|b\right|}^2$