Question

Can somebody help me with this question?

Answer 1

`(2)/(5)\vec{a}+\vec{b}`

Explanation:

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

`=(3)/(5)\vec{OB}+(1)/(5)\vec{BC}`
`\left\{OD:DB=2:3,BE:EC=1:4\right\}`

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

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

`=(2)/(5)\vec{a}+(2)/(5)\vec{b}+(3)/(5)\vec{b}`

`=(2)/(5)\vec{a}+\vec{b}`

I hope this helps you

:)