The vector is parallel to the plane.
Work Step by Step
Apply orthogonality test. This implies $n \cdot v=\lt 2,1,0 \gt \cdot \lt 2,-4,1 \gt$ or, $n \cdot v=2(2)+1(-4)+0(1)=0$ This means that the vector $v$ is orthogonal to the normal plane's normal vector $n$. Therefore, the vector is parallel to the plane.