Question

1. which pair of lines are perpendicular? ( overleftrightarrow{mn} ) and ( overleftrightarrow{po} ) ( overleftrightarrow{mn} ) and ( overleftrightarrow{rs} ) ( overleftrightarrow{mn} ) and ( overleftrightarrow{mq} ) ( overleftrightarrow{qr} ) and ( overleftrightarrow{ts} )

Explanation:

Step1: Recall the definition of perpendicular lines

Perpendicular lines intersect at a right - angle ($90^{\circ}$).

Step2: Analyze each option

• For $\overleftrightarrow{MN}$ and $\overleftrightarrow{PO}$: In a cube, $\overleftrightarrow{MN}\parallel\overleftrightarrow{PO}$ (they are opposite sides of a rectangular face of the cube - like structure), so they are not perpendicular.
• For $\overleftrightarrow{MN}$ and $\overleftrightarrow{RS}$: $\overleftrightarrow{MN}\parallel\overleftrightarrow{RS}$ (by the properties of parallel lines in 3 - D geometry for such a cuboid - like figure), so they are not perpendicular.
• For $\overleftrightarrow{MN}$ and $\overleftrightarrow{MQ}$: $\overleftrightarrow{MN}$ and $\overleftrightarrow{MQ}$ intersect at a right - angle. Since $MN$ is a horizontal edge (in its respective face) and $MQ$ is a vertical edge (in its respective face) of the cuboid - like figure, they form a $90^{\circ}$ angle.
• For $\overleftrightarrow{QR}$ and $\overleftrightarrow{TS}$: $\overleftrightarrow{QR}\parallel\overleftrightarrow{TS}$ (by the properties of parallel lines in 3 - D geometry for such a cuboid - like figure), so they are not perpendicular.

Answer:

$\overleftrightarrow{MN}$ and $\overleftrightarrow{MQ}$