Question

part 2 of 3
(b) the intersection of two distinct lines is a point.
part 3 of 3
(c) the intersection of three distinct planes is a line.

Explanation:

• For two distinct lines: In a plane, two distinct non - parallel lines intersect at a point. But in 3 - D space, two distinct lines can be skew (no intersection). So the intersection of two distinct lines is sometimes a point.
• For three distinct planes: Three distinct planes can intersect at a point (e.g., the three coordinate planes \(x = 0\), \(y=0\), \(z = 0\) in 3 - D space intersect at the origin \((0,0,0)\)), or a line (e.g., three planes that all contain the same line), or be parallel (no intersection). So the intersection of three distinct planes is sometimes a line.

Answer:

(b) Sometimes true
(c) Sometimes true