Question

Answer 1

\(\left|\overrightarrow{AB}+\overrightarrow{BC}\right|=\left|\overrightarrow{AC}\right|=AC=a\)

Gọi M là trung điểm AC \(\Rightarrow BM=\dfrac{a\sqrt{3}}{2}\) (trung tuyến tam giác đều)

\(\left|\overrightarrow{AB}-\overrightarrow{BC}\right|=\left|-\overrightarrow{AB}+\overrightarrow{BC}\right|=\left|\overrightarrow{BA}+\overrightarrow{BC}\right|=\left|2\overrightarrow{BM}\right|=2BM=2.\dfrac{a\sqrt{3}}{2}=a\sqrt{3}\)