(a) The planes P1 : 2x – y + 2z = 5 and P2 : x + 2y + 2z = 3 intersect in a line. (i) Find two points on this line. (ii) Find a third plane that contains this line, and is perpendicular to the plane...

Extracted text: (a) The planes P1 : 2x – y + 2z = 5 and P2 : x + 2y + 2z = 3 intersect in a line. (i) Find two points on this line. (ii) Find a third plane that contains this line, and is perpendicular to the plane x+y-2z = 1. (iii) Find the collection of lines in the xy-plane that represent the collection of all points in the xy-plane that are equidistant from the planes P1 and P2. (Your lines can be in the form ax + by = c.)