Equation of a line passing through a given point, perpendicular with a vector

Question

Find the line that goes through A(1,0,2) and is perpendicular to r = (-2,3,4) + s (1,1,2)

I did a bunch of work, but I don't know if any of it is right. I erased most of it, but this is what I came up with, which is wrong. Answer is: r = (1,0,2) + t(-11,7,2)

my work:

Answer 1

Consider the vector from A to the generic point $(-2+s,3+s,4+2s)$ of $r$ and equal the dot product of this and $(1,1,2)$ to $0$.
Found the value of $s$, substitute in the above vector: rescale if you want $(-11,7,2)$, every other parallel vector is good.