Answer
The vector is parallel to the plane.
Work Step by Step
We use the orthogonality test:
$n \cdot v=\lt 2,1,0 \gt \cdot \lt 2,-4,1 \gt$
or, $=2(2)+1(-4)+0(1)$
or, $n \cdot v =0$
This implies that the vector $v$ is orthogonal to the plane's normal vector $n$.
Hence, the vector is parallel to the plane because we have $n \cdot v =0$
