Calculate a vector that is perpendicular to Oy axis. Find a vector perpendicular to $Oy$ axis. Knowing that $v\cdot v_1=8$ and $v\cdot v_2=-3$, where $v_1=(3,1,-2)$ and $v_2=(-1,1,1)$

ley $v=(x,y,z)$ perpendicular to $OY$ axis means that
   $v*(0,1,0)=0$
$v*v_1=3*x+1*y-2*z=8$
$v*v_2=-1*x+1*y+1*z=-3$
$v*(0,1,0)=0 -->y=0$
so $3*x-2*z=8$
$-x+z=-3$   from second   $z=-3+x$ put into first one
$3*x-2*(-3+x)=8$
 $x=2$  and $z=-1$ so we have
$v=(2,0,-1)$
