Find a perpendicular foot and reflect a point in a line

Relative to O, A,B,C have position vectors $5\mathbf i+4\mathbf j+10\mathbf k$, $-4\mathbf i+4\mathbf j-2\mathbf k$, $-5\mathbf i+9\mathbf j+5\mathbf k$.

(i) Find the Cartesian equation of AB.3 marks

(ii) Find the length of projection of AC onto AB.3 marks

(iii) Hence or otherwise find the perpendicular distance from C to AB and the position vector of its perpendicular foot N.6 marks

(iv) D lies on CN produced such that N is the midpoint of CD. Find the position vector of D.2 marks