Cho tam giác ABC. Tính tổng ((AB) ,(BC) )+((BC) ,(CA) )+((CA) ,(AB) ) A. 180độ B. 360độ

* Hướng dẫn giải

Ta có $\left\{\begin{array}{l}\left(\overrightarrow{AB},\overrightarrow{BC}\right)={180}^0-\widehat{ABC}\\ \left(\overrightarrow{BC},\overrightarrow{CA}\right)={180}^0-\widehat{BCA}\\ \left(\overrightarrow{CA},\overrightarrow{AB}\right)={180}^0-\widehat{CAB}\end{array}\right.$

$\begin{array}{l}\Rightarrow \left(\overrightarrow{AB},\overrightarrow{BC}\right)+\left(\overrightarrow{BC},\overrightarrow{CA}\right)+\left(\overrightarrow{CA},\overrightarrow{AB}\right)={540}^0-\left(\widehat{ABC}+\widehat{BCA}+\widehat{CAB}\right)\\ ={540}^0-{180}^0={360}^0.\end{array}$

Chọn B.