The co-ordinates of three points are A(-1, -2, 1), B(-3, 4, -5), C(0, -2, 4).
(i) Find a vector equation of the line AB.
(ii) Find the co-ordinates of the mid-point M of AB.
(iii) The point N lies on BC. Given that $ \vert \overrightarrow {AB} \vert = \vert \overrightarrow {NC} \vert$, find the equation of the line MN.
I have done part i and ii, I don't know how to do part iii. Also in the vectors I don't know how to write it but the arrow should go above both letters in question iii.
for i) we get $$[x,y,z]=[-1;-2;1]+t[-2;6;-6]$$ fir ii) we have $$M\left(\frac{-1-3}{2};\frac{-2+4}{2};\frac{1-5}{2}\right)$$ for iii) I habe $$\vec{AB}=(-2;6;6)$$ and $$\vec{NC}=(-x;-2-y;4-z)$$