A plane through the origin is perpendicular to the plane $2x-y-z=5$ and parallel to the line joining the points $(1,2,3)$ and $(4,-1,2)$. Find the equation of the plane.
Analyzing this problem I found that the normal vector of the required plane is perpendicular to the line parallel to the plane. And, the given plane's normal vector is parallel to the line. I am stuck after this. Can I do a cross product between the vector formed by the two points and the normal vector of the given plane?