Getting the intersection of a line and a plain

Question

My line (2,1,10) goes through the plain with the normal (-2,3,8).

Now I would like to calculate the intersection with following formula

The resulting equation system supposed to be

Which I don't understand. How is (0,1,10) on the right side of the equation?

Answer 1

I think you gave a wrong hypothesis: the line passes by the point $(2,1,10)$ and parallel to the vector $(2,-3,8)^T$ and the plane passes by the point $(2,0,0)$ and parallel to the plane spanned by the vectors $(2,4,1)^T$ and $(-1,2,1)^T$. From this hypothesis we get the given system of equations.