Question

in the cube shown below, which lines are skew? ij and ik ij and kl ij and mn ko and mn

Explanation:

Step1: Recall skew - lines definition

Skew lines are non - parallel and non - intersecting lines in 3 - D space.

Step2: Analyze each pair

• For a cube, consider the relative positions of the lines.
• $\overrightarrow{IJ}$ and $\overrightarrow{KL}$: These lines are parallel as they are opposite sides of a face of the cube.
• $\overrightarrow{IJ}$ and $\overrightarrow{MN}$: $\overrightarrow{IJ}$ lies in one face and $\overrightarrow{MN}$ lies in a non - parallel face, they do not intersect and are not parallel, so they are skew.
• $\overrightarrow{KO}$ and $\overrightarrow{MN}$: These lines are in the same plane (a diagonal plane of the cube), so they are not skew.

Answer:

$\overrightarrow{IJ}$ and $\overrightarrow{MN}$