Construct a line equidistant from two perpendicular planes

A=(0,2,0), B=(1,0,2), and plane π1 is $\mathbf r\cdot(2,2,1)=4$.

(i) Find a vector equation of AB.2 marks

(ii) Show AB lies in π1.1 mark

(iii) Plane π2 contains AB and is perpendicular to π1. Show its equation is $\mathbf r\cdot(-2,1,2)=2$.3 marks

(iv) P=(p,0,0) is equidistant from π1,π2. Calculate p.5 marks

(v) Hence write down a line equidistant from π1,π2 which does not intersect either plane.2 marks