given that $\displaystyle \vec{v}\in \mathbb{R}^4$

and meets the requirements:

$\displaystyle \vec{v}\cdot \vec{e_{2}}<0 , $

$\displaystyle (\vec{e}_2+\vec{e}_4)\cdot \vec{v}=0$

$\displaystyle \vec{e}_1 \cdot \vec{v}=\vec{e}_4\cdot \vec{v}$

$\displaystyle (\vec{e}_2+\vec{e}_3)\cdot \vec{v}=0$

$\displaystyle \left \| \vec{v} \right \| = 6$

Find the vector $\displaystyle \vec{v}$ (If exists)

Can some one please help me here?

Thank you!