Question

Can somebody help me with this question?

Answer 1

Answer:

$\frac{2}{5}\vec{a}+\vec{b}$

Step-by-step explanation:

$\vec{DE}=\vec{DB}+\vec{BE}$

      $=\frac{3}{5}\vec{OB}+\frac{1}{5}\vec{BC}$                $\left\{OD:DB=2:3,BE:EC=1:4\right\}$

      $=\frac{3}{5}\left(\vec{OA}+\vec{AB}\right)+\frac{1}{5}\left(\vec{BA}+\vec{AO}+\vec{DC}\right)$

      $=\frac{3}{5}\left(\vec{a}+\vec{b}\right)+\frac{1}{5}\left(-\vec{b}-\vec{a}+\vec{3b}\right)$

      $=\frac{2}{5}\vec{a}+\frac{2}{5}\vec{b}+\frac{3}{5}\vec{b}$

      $=\frac{2}{5}\vec{a}+\vec{b}$

I hope this helps you

:)