Question: Area Intersection Point with vector

Hello
I am a bit further with my initial vector question. I managed to decompose the vectors and set them as equations for each dimension (x, y, z) and solve a system of equations with the variables of the parametric surface and the parametric line (black). The goal is to calculate P (intersection with the surface) and, from there, the vector V1. The problem is that I always get zero as the solution for all the variables. 
Any help would be greatly appreciated! Thanks.question_surface_.mw
 

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