Question

how do you see it? consider the lines that contain the segments in the figure and the planes that contain the faces of the figure. all angles are right angles. identify which lines have the following properties. a. parallel to $overleftrightarrow{nq}$ b. intersect $overleftrightarrow{nq}$ c. skew to $overleftrightarrow{nq}$

Explanation:

Step1: Recall parallel - line definition

Parallel lines in 3 - D are lines that lie in the same plane and do not intersect. In a cube, edges that are in the same - direction are parallel. For a line like $\overleftrightarrow{NQ}$, the parallel lines are $\overleftrightarrow{MP}$, $\overleftrightarrow{KL}$, $\overleftrightarrow{RS}$.

Step2: Recall intersecting - line definition

Intersecting lines meet at a single point. Lines that share a common vertex with $\overleftrightarrow{NQ}$ are $\overleftrightarrow{NK}$, $\overleftrightarrow{NM}$, $\overleftrightarrow{QP}$, $\overleftrightarrow{QR}$.

Step3: Recall skew - line definition

Skew lines are non - parallel and non - intersecting lines that do not lie in the same plane. For $\overleftrightarrow{NQ}$, the skew lines are $\overleftrightarrow{KR}$, $\overleftrightarrow{LS}$, $\overleftrightarrow{PS}$, $\overleftrightarrow{LM}$.

Answer:

a. $\overleftrightarrow{KL}$, $\overleftrightarrow{MP}$, $\overleftrightarrow{RS}$
b. $\overleftrightarrow{NK}$, $\overleftrightarrow{NM}$, $\overleftrightarrow{QP}$, $\overleftrightarrow{QR}$
c. $\overleftrightarrow{KR}$, $\overleftrightarrow{LS}$, $\overleftrightarrow{PS}$, $\overleftrightarrow{LM}$