I have $\vec{a}$ and $\vec{b}$. Need to find $\vec{x}$ if $[\vec{x},\vec{a}]=\vec{b}$
Let $\vec{x}=(x,y,z)$. Then $[\vec{x},\vec{a}]=(ya_z-za_y;za_x-xa_z;xa_y-ya_x)=(b_x;b_y;b_z)$ We have the system, where $a_x,a_y,a_z,b_x,b_y,b_z$ we know: $$ya_z-za_y=b_x$$ $$za_x-xa_z=b_y$$ $$xa_y-ya_x=b_z$$ (right?)
How to solve it (Find $x,y,z$)