Given that the vectors [tex]\(\overrightarrow{PQ}\)[/tex] and [tex]\(\overrightarrow{RS}\)[/tex] intersect to form four right angles, let's analyze what this information implies.
When two vectors intersect to form four right angles, each of the angles formed at the intersection point is [tex]\(\frac{\pi}{2}\)[/tex] radians (90 degrees). This means that the two vectors are perpendicular to each other.
Let's review the options provided:
A. [tex]\(\overrightarrow{PQ} \perp \overrightarrow{RS}\)[/tex]
B. [tex]\(\overrightarrow{PQ}\)[/tex] and [tex]\(\overrightarrow{RS}\)[/tex] are skew
C. [tex]\(\overrightarrow{PQ}\)[/tex] and [tex]\(\overrightarrow{RS}\)[/tex] are parallel
D. [tex]\(\overrightarrow{PQ} = \overrightarrow{RS}\)[/tex]
Given that the vectors intersect to form right angles, option A is indeed the correct statement. Perpendicular vectors intersect at right angles. Skew vectors do not intersect at all, so B is incorrect. Parallel vectors run in the same or opposite directions but never intersect to form right angles, making C incorrect. If [tex]\(\overrightarrow{PQ}\)[/tex] were equal to [tex]\(\overrightarrow{RS}\)[/tex], they would overlap completely, which does not describe the scenario of forming four right angles, making D incorrect.
Therefore, the true statement is:
A. [tex]\(\overrightarrow{PQ} \perp \overrightarrow{RS}\)[/tex]
