Reflect a plane by retaining its intersection and reflecting one point

A,B have position vectors $\mathbf i-2\mathbf j-\mathbf k$ and $-\mathbf i-2\mathbf k$. Line l1 goes through A parallel to $5\mathbf i+2\mathbf j-\mathbf k$. Plane Π1 is $\mathbf r\cdot(-1,1,2)=3$.

(i) Find the acute angle between l1 and Π1.2 marks

(ii) Find the position vector of the perpendicular foot N from B to Π1. Hence find the reflected point B′.4 marks

Plane Π2 contains B and l1.

(iii) Find Π2 in scalar-product form.3 marks

(iv) Find the Cartesian equation of intersection l2 of Π1,Π2.2 marks

(v) Π3 is the reflection of Π2 in Π1. Find an equation $\mathbf r=\mathbf u+s\mathbf p+t\mathbf q$, with s,t real.2 marks