Question

Cho hình lập phương ABCD.EFGH. Phân tích vecto AE theo vecto AC, AF, AH

Answer 1

\(\overrightarrow{AF}=\overrightarrow{AE}+\overrightarrow{AB}\)

\(\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{AD}\)

\(\overrightarrow{AH}=\overrightarrow{AE}+\overrightarrow{AD}\)

\(\Rightarrow\overrightarrow{AF}-\overrightarrow{AC}+\overrightarrow{AH}=\overrightarrow{AE}+\overrightarrow{AB}-\overrightarrow{AB}-\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AD}\)

\(\Rightarrow\overrightarrow{AE}=\dfrac{1}{2}\overrightarrow{AF}-\dfrac{1}{2}\overrightarrow{AC}+\dfrac{1}{2}\overrightarrow{AH}\)