(1) describe and sketch all possible types of intersections of two planes in r 3 .
(2) eliminate variables to determine if each pair of planes in the list below, define the same plane, intersect in a line or do not intersect. if the pair intersects in a line find parametric equations for the line of intersection. (a) 3x − 2y + z = 2 (b) 2x + y − z = 2 (c) −x + 3y + 2z = 4 (d) 4x + 2y − 2z = 4 (e) −6x + 4y − 2z = −2
(3) eliminate variables to determine if each triple of planes in problem 2, define the same plane, intersect in a line, intersect in one point or do not intersect. if the triple intersects in a line find parametric equations for the line of intersection. if the triple intersect at one point find the point. (4) use the parametric equations for the line of intersection of the planes (a) and (b) in problem 2 to find the intersection of this line with the planes defined by (c), (d) and (e). compare this with the answers in problem 3 you obtained by eliminating variables.