Question

Giúp mình câu 3b với ạ

Answer 1

a: Xét ΔBAC vuông tại A có cos B=AB/BC

=>a/BC=1/2

=>BC=2a

=>AC=a căn 3

\(\overrightarrow{AC}\cdot\overrightarrow{CB}=-\overrightarrow{CA}\cdot\overrightarrow{CB}=-CA\cdot CB\cdot cosC=-a\sqrt{3}\cdot2a\cdot\dfrac{\sqrt{3}}{2}\)

\(=-3a^2\)

b: \(\overrightarrow{AB}\cdot\overrightarrow{IC}=\overrightarrow{AB}\cdot\overrightarrow{AC}-\overrightarrow{AB}\cdot\overrightarrow{AI}\)

\(=0-AB\cdot AI\cdot cos60=-a\cdot a\cdot\dfrac{1}{2}=-\dfrac{1}{2}a^2\)

\(\overrightarrow{AB}\cdot\overrightarrow{IM}=\overrightarrow{AB}\cdot\overrightarrow{AM}-\overrightarrow{AB}\cdot\overrightarrow{AI}\)

\(=0-AB\cdot AI\cdot cosBAI=-a\cdot a\cdot\dfrac{1}{2}=-\dfrac{1}{2}a^2\)