Finding parallel vectors

Question

In ABC , D is a point on BC such that BD:DC = 2:1 . DE is parallel to BA and FE is parallel to BC. It is given that BA = 4a , BC = 6b , AD= 4b - 4a . Show that DE = $4/3$ a

How do I find DE ?

DE = DF + FE

DE = DA + AE

I do not have a complete set of information to find DE. what is the other method ? I Guess it's using The information on DE is parallel to BA ?

DE = k (4a) , where K is a constant

From here I'm not too sure how to carry on . Thanks in advance !

Answer 1

If DE is parallel to AB, then the length of DE is proportional to AB as DC is proportional to BC.

Answer 2

Hint:

By construction $ABC$ is similar to $DEC$, so: $$ BA : BC=DE:DC $$ and $BA=4a$, $BC=6b$, $DC=2b$.