Equation of the Plane Passing Through Two Points and is Perpendicular to a Given Plane

How do we find an equation of the plane passing through two points and is perpendicular to a given plane?
In general, when we want to find an equation of a plane, we need to know a point lying in the plane, and the normal vector of the plane (which is perpendicular to the plane). We already have a point, all we need is the vector normal to the plane.
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