Question

cho \(\Delta ABC\). Tổng \(\left(\overrightarrow{AB},\overrightarrow{BC}\right)+\left(\overrightarrow{BC},\overrightarrow{CA}\right)+\left(\overrightarrow{CA},\overrightarrow{AB}\right)\) có thể chấp nhận giá trị nào trong các giá trị sau : \(90^o;180^o;270^o;360^o\) ?

Answer 1

Ta có : \(\left(\overrightarrow{AB},\overrightarrow{BC}\right)+\left(\overrightarrow{BA},\overrightarrow{BC}\right)=180^o;\left(\overrightarrow{BC},\overrightarrow{CA}\right)+\left(\overrightarrow{CB},\overrightarrow{CA}\right)=180^o\)

\(\left(\overrightarrow{CA},\overrightarrow{AB}\right)+\left(\overrightarrow{AC},\overrightarrow{AB}\right)=180^o\)

Mà \(\left(\overrightarrow{BA},\overrightarrow{CB}\right)+\left(\overrightarrow{CB},\overrightarrow{CA}\right)+\left(\overrightarrow{AC},\overrightarrow{AB}\right)=\widehat{A}+\widehat{B}+\widehat{C}\)\(=180^o\)

Do vậy tổng:  \(\left(\overrightarrow{AB},\overrightarrow{BC}\right)+\left(\overrightarrow{BC},\overrightarrow{CA}\right)+\left(\overrightarrow{CA},\overrightarrow{AB}\right)=360^o\)