Locate a perpendicular foot and reflect a whole line

(i) Find a vector equation of the line through the points $A$ and $B$ with position vectors $7\mathbf i+8\mathbf j+9\mathbf k$ and $-\mathbf i-8\mathbf j+\mathbf k$ respectively.

(ii) The perpendicular to this line from the point $C$ with position vector $\mathbf i+8\mathbf j+3\mathbf k$ meets the line at the point $N$. Find the position vector $N$ and the ratio of $AN:NB$.

(iii) Find a Cartesian equation of the line which is a reflection of the line $AC$ in the line $AB$.