Reflect a point in a line and calculate the resulting area

Relative to O, A,B have position vectors $4\mathbf i+3\mathbf j$ and $5\mathbf i+7\mathbf j$. Line $l_1$ passes through B parallel to $\mathbf i+2\mathbf j+\alpha\mathbf k$. Line $l_2$ has Cartesian equation $(1-x)/2=(z-2)/1$, y=4.

(i) Given $l_1,l_2$ are perpendicular, show α=2.2 marks

(ii) Find the length of projection of BA onto $l_1$. Hence find vector BN, where N is the perpendicular foot from A onto $l_1$.4 marks

(iii) A′ is the reflection of A in $l_1$, and C makes AA′CB a parallelogram. Find its exact area.3 marks