Question

in the cube shown below, which lines are intersecting? be and cd, ei and gh, dh and fi, hi and dh

Explanation:

Step1: Recall definition of intersecting lines

Intersecting lines meet at a point.

Step2: Analyze each option

• For $\overrightarrow{BE}$ and $\overrightarrow{CD}$: They are skew - not in the same plane and do not intersect.
• For $\overrightarrow{EI}$ and $\overrightarrow{GH}$: They are skew - not in the same plane and do not intersect.
• For $\overrightarrow{DH}$ and $\overrightarrow{FI}$: They are skew - not in the same plane and do not intersect.
• For $\overrightarrow{HI}$ and $\overrightarrow{DH}$: They share the common point $H$, so they intersect.

Answer:

$\overrightarrow{HI}$ and $\overrightarrow{DH}$