Question

Explain why two skew lines do not determine a plane.

Short answer

Two skew lines don't determine a plane.

Step-by-step solution

Given information

The two skew lines ${\mathfrak{L}}_1$ and ${\mathfrak{L}}_2$

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 ${\mathfrak{L}}_1$and ${\mathfrak{L}}_2$are skew. It means that lines ${\mathfrak{L}}_1$and ${\mathfrak{L}}_2$neither intersect nor are parallel.

Calculation

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

Therefore, if the lines ${\mathfrak{L}}_1$ and ${\mathfrak{L}}_2$ are skew; they are not in a single plane.

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