Question

in the cube shown below, which lines are intersecting? select all that apply.

Explanation:

Step1: Recall definition of intersecting lines

Intersecting lines meet at a point.

Step2: Analyze $\overrightarrow{HI}$ and $\overrightarrow{IJ}$

They meet at point $I$. So they are intersecting.

Step3: Analyze $\overrightarrow{GJ}$ and $\overrightarrow{GK}$

They meet at point $G$. So they are intersecting.

Step4: Analyze $\overrightarrow{GJ}$ and $\overrightarrow{IJ}$

They are on different - parallel planes and do not meet. So they are not intersecting.

Step5: Analyze $\overrightarrow{JN}$ and $\overrightarrow{KN}$

They are on different - parallel planes and do not meet. So they are not intersecting.

Answer:

$\overrightarrow{HI}$ and $\overrightarrow{IJ}$, $\overrightarrow{GJ}$ and $\overrightarrow{GK}$