Find all vectors v such that the resultant of $\langle2,3,0 \rangle$, $\langle0,6,1 \rangle$, $\langle2,0,-4 \rangle$ and v is parallel to the x-y plane.
For these vectors' resultant to be parallel to x-y plane, we want
$\langle 2,3,0 \rangle $ + $\langle0,6,1 \rangle$ + $\langle2, 0,-4 \rangle$ + $\langle a,b,c \rangle $ = $\langle 4+a,9+b,-3+c \rangle$ parallel to x-y plane where v = $\langle a,b,c \rangle $ which is possible only when v = $\langle a,b,3\rangle$ where $a,b\in R$
Is this correct?