Consider three planes P_1 : x - y + z = 1, P_2 : x + y - z = -1 and P_3 : x - 3y + 3z…

MATHEMATICS · Subjective · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

Consider three planes

P_1 : x - y + z = 1, P_2 : x + y - z = -1

\text{and } P_3 : x - 3y + 3z = 2

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, P_1

and

P_2

, respectively. Statement I At least two of the lines

L_1, L_2

and

L_3

are non-parallel. Statement II The three planes do not have a common point.