Rotate Point Between Coordinate Systems

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I have a point(s)

P0(x,y,z)...Pn(x,y,z)

and a plane described by two vectors and a normal.

V1(x,y,z)

V2(x,y,z)

N1(x,y,z)

I am rotating them so that they are axis aligned in the world by doing this

P0'=(P0 DOT(V1),P0 DOT(V2), P0 DOT(N1))

This works and the points are rotated as expected. I want to know how to now rotate them, and new points back. Basically the inverse operation

Thanks