Question

Answer 1

a: \(\overrightarrow{AB}\cdot\overrightarrow{AC}=a\cdot a\cdot\cos60^0=\dfrac{a^2}{2}\)

b: \(\overrightarrow{AH}\cdot\overrightarrow{AC}=AH\cdot AC\cdot\cos30^0=\dfrac{a\sqrt{3}}{2}\cdot a\cdot\dfrac{\sqrt{3}}{2}=\dfrac{3a^2}{4}\)

c: \(\overrightarrow{AB}\left(\overrightarrow{AB}+\overrightarrow{AC}\right)=AB\cdot AB\cdot\cos0^0+\dfrac{a^2}{2}=\dfrac{3}{2}a^2\)

Answer 2

Bổ sung phần d:

d, \(\overrightarrow{AC}\cdot\left(\overrightarrow{AC}-\overrightarrow{AB}\right)=\overrightarrow{AC}^2-\overrightarrow{AC}\cdot\overrightarrow{AB}=a^2-\dfrac{a^2}{2}=\dfrac{a^2}{2}\)

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