Chapter 6.3, Problem 20WE

To determine

To show: $\overleftrightarrow{RT}$ and $\overleftrightarrow{SW}$ are skew lines.

Answer to Problem 20WE

  $\overleftrightarrow{RT}$ and $\overleftrightarrow{SW}$ are skew lines.

Explanation of Solution

Four points $R,\text{ S, }T,\text{ and }W$ also $\overleftrightarrow{RS}\text{ and }\overleftrightarrow{TW}$ are skew.

  

The lines $\overleftrightarrow{RS}\text{ and }\overleftrightarrow{TW}$ are skew if and only if they are not coplanar.

Clearly we can see that there are no intersection point between $\overleftrightarrow{RT}$ and $\overleftrightarrow{SW}$ lines.

Therefore, the lines $\overleftrightarrow{RT}$ and $\overleftrightarrow{SW}$ are skew lines.