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Chapter 10: Q 56. (page 847)

Let L1 and L2 be two skew lines. Prove that no plane contains both L1 and L2

Short Answer

Expert verified

There is no plane that contains two skew lines L1and L2

Step by step solution

01

Given information

The two skew lines L1 and L2

02

Calculation

The goal is to demonstrate that no plane contains both L1 and L2

Use the skew line definition to demonstrate the effect.

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

The lines L1 and L2 are skew. It means that lines L1 and L2 neither intersect nor are parallel.

03

Calculation

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

Therefore, if the lines L1and L2are skew; they are not in a single plane.

Thus, there is no plane that contains two skew lines L1and L2

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