Answer:
[tex]\frac{2}{5}\vec{a}+\vec{b}[/tex]
Step-by-step explanation:
[tex]\vec{DE}=\vec{DB}+\vec{BE}[/tex]
[tex]=\frac{3}{5}\vec{OB}+\frac{1}{5}\vec{BC}[/tex] [tex]\left\{OD:DB=2:3,BE:EC=1:4\right\}[/tex]
[tex]=\frac{3}{5}\left(\vec{OA}+\vec{AB}\right)+\frac{1}{5}\left(\vec{BA}+\vec{AO}+\vec{DC}\right)[/tex]
[tex]=\frac{3}{5}\left(\vec{a}+\vec{b}\right)+\frac{1}{5}\left(-\vec{b}-\vec{a}+\vec{3b}\right)[/tex]
[tex]=\frac{2}{5}\vec{a}+\frac{2}{5}\vec{b}+\frac{3}{5}\vec{b}[/tex]
[tex]=\frac{2}{5}\vec{a}+\vec{b}[/tex]
I hope this helps you
:)
