High School

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L₁ and L₂ are two skew lines. How many lines joining L₁ and L₂ can be drawn such that the line is perpendicular to both L₁ and L₂?

A. 0
B. 1
C. 2
D. Infinite

Answer :

Final answer:

(b) 1, indicating that only one line can be drawn joining L₁ and L₂ that is perpendicular to both. The correct answer is (b) 1

Explanation:

Skew lines, by definition, do not intersect and are not parallel. The line joining them that is perpendicular to both is unique and represents the shortest distance between the skew lines. This unique line forms right angles with both L₁ and L₂, making it the only line that satisfies the condition. Thus, option (b) is the correct choice, reflecting the geometric properties of skew lines and their perpendicular relationships.

Understanding the geometric properties of skew lines is essential to solving problems involving their relationships. While skew lines don't intersect, there's precisely one line perpendicular to both, representing the shortest distance between them. This perpendicularity ensures that the line forms right angles with both skew lines, providing a clear geometric interpretation. Hence, the answer (b) 1 accurately represents this unique characteristic of skew lines and their perpendicular relationships in three-dimensional space.

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