To determine the correct relationship between [tex]\(\overrightarrow{PQ}\)[/tex] and [tex]\(\overrightarrow{RS}\)[/tex], let's analyze the given information step-by-step.
1. Intersection Forming Four Right Angles:
- When two lines intersect to form four right angles, they meet at a point and are perpendicular to each other.
- Forming right angles means that each angle is [tex]\(90^\circ\)[/tex].
2. Understanding the Choices:
- A. [tex]\(\overrightarrow{PQ}\)[/tex] and [tex]\(\overrightarrow{RS}\)[/tex] are skew:
- Skew lines are lines that do not intersect and are not parallel. This contradicts the given as we know [tex]\(\overrightarrow{PQ}\)[/tex] and [tex]\(\overrightarrow{RS}\)[/tex] intersect.
- B. [tex]\(\overrightarrow{PQ}\)[/tex] and [tex]\(\overrightarrow{RS}\)[/tex] are parallel:
- Parallel lines do not intersect and maintain a constant distance apart. This also contradicts the information given, where the lines do intersect.
- C. [tex]\(\overrightarrow{PQ} \perp \overrightarrow{RS}\)[/tex]:
- Perpendicular lines intersect at a point and form four right angles. This aligns perfectly with our analysis.
- D. [tex]\(\overrightarrow{PQ} = \overrightarrow{RS}\)[/tex]:
- For two vectors to be equal, each corresponding component must also be equal. This would imply they are the same line, not forming right angles but overlapping.
3. Conclusion:
- Based on the given information and our analysis, the correct statement is:
- C. [tex]\(\overrightarrow{PQ} \perp \overrightarrow{RS}\)[/tex].
So the correct answer is: [tex]\(\overrightarrow{PQ} \perp \overrightarrow{RS}\)[/tex].
