Question

ДАЮ 100 БАЛЛОВ. ПОЖАЛУЙСТА ПОМОГИТЕ! ​

Answer 1

Ответ:

$1)\ \ \overline{AO}=\dfrac{1}{2}\cdot \overline{AC}=\dfrac{1}{2}\cdot (\overline{a}+\overline{b})\\\\\\2)\ \ \overline{CK}=\overline{CB}+\overline{BK}=-\overline{b}-\dfrac{3}{4}\cdot \overline{a}\\\\\overline{CE}=\overline{CD}+\overline{DE}=-\overline{a}-\dfrac{1}{5}\cdot \overline{b}\\\\\overline{KE}=\overline{KC}+\overline{CE}=\overline{b}+\dfrac{3}{4}\cdot \overline{a}-\overline{a}-\dfrac{1}{5}\cdot \overline{b}=\dfrac{4}{5}\cdot \overline{b}-\dfrac{1}{4}\cdot \overline{a}$

$3)\ \ \overline{AF}=\dfrac{4}{5}\cdot (\overline{a}+\overline{b})\\\\\overline{AM}=\overline{AB}+\overline{BM}=\overline{a}+\dfrac{1}{4}\cdot \overline{b}\\\\\overline{AN}=\overline{AD}+\overline{DN}=\overline{b}+\dfrac{1}{2}\cdot \overline{a}\\\\\overline{MF}=\overline{MC}+\overline{CF}=\dfrac{3}{4}\cdot \overline{b}-\dfrac{1}{5}\cdot (\overline{a}+\overline{b})=\dfrac{11}{20}\cdot \overline{b}-\dfrac{1}{5}\cdot \overline{a}$

$\overline{NF}=\overline{NC}+\overline{CF}=\dfrac{1}{2}\cdot \overline{a}-\dfrac{1}{5}\cdot (\overline{a}+\overline{b})=\dfrac{3}{10}\cdot \overline{a}-\dfrac{1}{5}\cdot \overline{b}\\\\\overline{MN}=\overline{AN}-\overline{AM}=\overline{b}+\dfrac{1}{2}\cdot \overline{a}-\overline{a}-\dfrac{1}{4}\cdot \overline{b}=\dfrac{3}{4}\cdot \overline{b}-\dfrac{1}{2}\cdot \overline{a}$

$\star \ \ \overline{MF}=\overline{MA}+\overline{AF}=-\overline{a}-\dfrac{1}{4}\cdot \overline{b}+\dfrac{4}{5}\cdot (\overline{a}+\overline{b})=-\dfrac{1}{5}\cdot \overline{a}+\dfrac{11}{20}\cdot \overline{b}\ \ \star$