Parallelogram and vectors

[123]

Given parallelogram ABCD. \(\displaystyle M\epsilon BC\), \(\displaystyle N\epsilon BA\), \(\displaystyle BM:MC=3:2\), \(\displaystyle BN=NA\). Also, \(\displaystyle \vec{AD}=\vec{a},\) \(\displaystyle \vec{DC}=\vec{b}.\)
Express the vector \(\displaystyle \vec{MN}\) vectors \(\displaystyle \vec{a}\) and \(\displaystyle \vec{b}\).

first, I draw it :lol: and stoped. how start?

 

[Deleted member 4993]

Given parallelogram ABCD. \(\displaystyle M\epsilon BC\), \(\displaystyle N\epsilon BA\), \(\displaystyle BM:MC=3:2\), \(\displaystyle BN=NA\). Also, \(\displaystyle \vec{AD}=\vec{a},\) \(\displaystyle \vec{DC}=\vec{b}.\)
Express the vector \(\displaystyle \vec{MN}\) vectors \(\displaystyle \vec{a}\) and \(\displaystyle \vec{b}\).

first, I draw it :lol: and stoped. how start?

BM:BC = 3:5 ? BM:AD = 3:5

and

BN:BA = 1: 2

Now think vector addition.

 

[123]

BM:BC = 3:5 ? BM:AD = 3:5

why 3:5?

 

[Deleted member 4993]

BM:BC = 3:5 ? BM:AD = 3:5

why 3:5?

Are you working with paper/pencil or just staring at the screen?

BM:BC = BMBM+MC) = 33+2) = 3:5

 

[123]

trying...
so, \(\displaystyle -\frac{3}{5}\vec{a}+\frac{1}{2}\vec{b}\)?

 

[Deleted member 4993]

trying...
so, \(\displaystyle -\frac{3}{5}\vec{a}+\frac{1}{2}\vec{b}\)?

Correct - why "?"!!!!!!