GMA Round 1 向量计算

传送门

向量计算

　　已知$left |overrightarrow{AB} ight |^2+left |overrightarrow{CD} ight |^2+left |overrightarrow{EF} ight |^2+overrightarrow{AB}cdot overrightarrow{CD}+overrightarrow{CD}cdot overrightarrow{EF}+overrightarrow{EF}cdot overrightarrow{AB}=18$

　　求$left | overrightarrow{AB}+overrightarrow{CD} ight |^2+ left | overrightarrow{CD}+overrightarrow{EF} ight |^2+ left | overrightarrow{EF}+overrightarrow{AB} ight |^2$

$left | overrightarrow{AB}+overrightarrow{CD} ight |^2+ left | overrightarrow{CD}+overrightarrow{EF} ight |^2+ left | overrightarrow{EF}+overrightarrow{AB} ight |^2$

$=left |overrightarrow{AB} ight |^2+left |overrightarrow{CD} ight |^2+2overrightarrow{AB}cdot overrightarrow{CD}+left |overrightarrow{CD} ight |^2+left |overrightarrow{EF} ight |^2+2overrightarrow{CD}cdot overrightarrow{EF}+left |overrightarrow{EF} ight |^2+left |overrightarrow{AB} ight |^2+2overrightarrow{EF}cdot overrightarrow{AB}$

$=2left |overrightarrow{AB} ight |^2+2left |overrightarrow{CD} ight |^2+2left |overrightarrow{EF} ight |^2+2overrightarrow{AB}cdot overrightarrow{CD}+2overrightarrow{CD}cdot overrightarrow{EF}+2overrightarrow{EF}cdot overrightarrow{AB}$

$=2*(left |overrightarrow{AB} ight |^2+left |overrightarrow{CD} ight |^2+left |overrightarrow{EF} ight |^2+overrightarrow{AB}cdot overrightarrow{CD}+overrightarrow{CD}cdot overrightarrow{EF}+overrightarrow{EF}cdot overrightarrow{AB})$

$=2*18$

$=36$

定位：简单题