# Thread: [SOLVED] Vector Proof - Parallelogram and Triangle

1. ## [SOLVED] Vector Proof - Parallelogram and Triangle

The quadrilateral OABC is a parallelogram, and $\displaystyle \vec{OC} = 3\vec{CD}$

Now, let $\displaystyle \vec{AE} = m \times \vec{OA}$ and $\displaystyle \vec{BE} = n \times \vec{DB}$, where $\displaystyle m, n \in R^+$. Find the value of $\displaystyle m$ and $\displaystyle n$.

I can't seem to find how to calculate $\displaystyle m$ and $\displaystyle n$, anyone know how to?

2. ## Similar Triangles

Hello Enedrox

Welcome to Math Help Forum!
Originally Posted by Enedrox

The quadrilateral OABC is a parallelogram, and $\displaystyle \vec{OC} = 3\vec{CD}$

Now, let $\displaystyle \vec{AE} = m \times \vec{OA}$ and $\displaystyle \vec{BE} = n \times \vec{DB}$, where $\displaystyle m, n \in R^+$. Find the value of $\displaystyle m$ and $\displaystyle n$.

I can't seem to find how to calculate $\displaystyle m$ and $\displaystyle n$, anyone know how to?
Note that triangles DCB, BAE and DOE are all similar, because of the parallel lines.

So $\displaystyle \vec{DO} = 4\vec{DC} \Rightarrow \vec{DE}=4\vec{DB}$

$\displaystyle \Rightarrow \vec{BE}=3\vec{DB}$

$\displaystyle \Rightarrow n = 3$

and $\displaystyle \vec{EO}=4\vec{BC}=4\vec{AO}$

$\displaystyle \Rightarrow \vec{AE} = 3\vec{OA}$

$\displaystyle \Rightarrow m = 3$