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Chapter 10: Q 12. (page 845)

Explain why two skew lines do not determine a plane.

Short Answer

Expert verified

Two skew lines don't determine a plane.

Step by step solution

01

Given information

The two skew lines L1 and L2

02

Calculation

The goal is to show why a plane cannot be determined by two skew lines.

Use the skew line definition to demonstrate the effect.

If the lines do not intersect or are not parallel, they are skewed.

The lines L1and L2are skew. It means that lines L1and L2neither intersect nor are parallel.

03

Calculation

The lines in a plane either intersect or run parallel to one another.

Therefore, if the lines L1 and L2 are skew; they are not in a single plane.

That's why two skew lines don't determine a plane.

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