Mathematics

Problem

Consider the planes

P_1: 2x + y + z + 4 = 0

P_2: y - z + 4 = 0

and

P_3: 3x + 2y + z + 8 = 0

Let

L_1, L_2, L_3

be the lines of intersection of the planes

P_2

and

P_3

P_3

and

P_1

, and

P_1

and

P_2

respectively. Then, a. at least two of the lines

L_1, L_2

and

L_3

are non-parallel b. at least two of the lines

L_1, L_2

and

L_3

are parallel c. the three planes intersect in a line d. the three planes form a triangular prism