Hi, I'm struggling to complete this question. I am required to find vectors $\vec{ED}$ and $\vec{EF}$ in terms of a and b.
I have so far found that vector $\vec{ED}$ = b - $\frac{5}{3}$a.
I would please like help in finding $\vec{EF}$. All advice really appreciated.
Thank you
Note that $AD||BF$ (since $AD||BC$ - these being the opposite sides of a parallelogram). $$$$Hence you can prove that $\Delta EFB$ is similar to $\Delta EDA$. $$$$Thus $$\dfrac{EB}{EA}=\dfrac{EF}{ED}=\dfrac25$$ $$\Rightarrow\vec{EF}=\dfrac25\vec{ED}=\dfrac25\left(\vec b-\frac53\vec a\right)=\dfrac25\vec{b}-\dfrac23\vec a$$