If [tex]$\overrightarrow{PQ}$[/tex] and [tex]$\overrightarrow{RS}$[/tex] intersect to form four right angles, which statement is true?

A. [tex]$\stackrel{PQ}{PQ}$[/tex]

B. [tex]$\overrightarrow{PQ} \perp \overleftrightarrow{RS}$[/tex]

C. [tex]$\overrightarrow{PQ}$[/tex] and [tex]$\overrightarrow{RS}$[/tex] are parallel

D. [tex]$\overrightarrow{PQ}$[/tex] and [tex]$\overrightarrow{RS}$[/tex] are skew



Answer :

When two lines intersect to form four right angles, it means they are perpendicular to each other. Intersecting lines that form right angles indicate 90-degree angles between them.

Thus, the correct statement corresponding to this geometric property is:
B. [tex]\( \overrightarrow{P Q} \perp \overleftrightarrow{R S} \)[/tex]

This means that [tex]\(\overrightarrow{P Q}\)[/tex] is perpendicular to [tex]\(\overleftrightarrow{R S}\)[/tex]. When two lines are perpendicular, they intersect such that the angle between them is 90 degrees at the point of intersection in all four divisions formed by the intersection.

In simpler terms, the two lines form an "L" shape in each quadrant, ensuring that the angle in each part is exactly 90 degrees (a right angle). Therefore, the appropriate choice is B.