1003040201

We are given the vectors $\overrightarrow{a}=(-1;2;3)$, $\overrightarrow{b}=(3;1;-2)$ and $\overrightarrow{c}=(1;2;-1)$. Find the coordinates of a vector $\overrightarrow{v}$, such that $\overrightarrow{v}$ is perpendicular to both vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, while $\overrightarrow{v}\cdot \overrightarrow{c}=12$ holds.