Project vector onto r-Z plane

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I have a normal vector 'n' in 3D space and the point on the surface from which is calculated in Cartesian coordinates x,y,z. I would like to project the point and the normal cylindrically onto the θ=0 plane following the rule (x,y,z) --> (r,Z)= =(sqrt{x^2+y^2} , z) in order to calculate the length of the normal vector before and after the projection. Is there an easy formula for this?