Q 13. Explain why any two skew lines l... [FREE SOLUTION]

Chapter 10: Q 13. (page 845)

Explain why any two skew lines lie on a unique pair of parallel planes.

Short Answer

Expert verified

Any point from line $L_{1}$ along with $N$ and any point from line $L_{2}$ along with $N$ determine the unique pair of parallel planes.

Step by step solution

Given information

The two skew lines $L_{1}$ and $L_{2}$

Calculation

Take a look at the two skew lines $L_{1}$ and $L_{2}$

The goal is to explain why two skew lines are parallel to each other on a single set of parallel 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 $L_{1}$ and $L_{2}$ are skew. It means that lines $L_{1}$ and $L_{2}$ neither intersect nor are parallel. Assume that $d_{1}$ and $d_{2}$ be the direction vectors of the skew lines $L_{1}$ and $L_{2}$

Calculation

Since, the lines are skew, therefore,

N = d_{1} 脳 d_{2} 鈮� 0

Therefore, any point from line $L_{1}$ along with $N$ and any point from line $L_{2}$ along with $N$ determine the unique pair of parallel planes.

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Explain why any two skew lines lie on a unique pair of parallel planes.

Short Answer

Step by step solution

Given information

Calculation

Calculation

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