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Identify one pair of intersecting lines in the diagram
line 3 and line 5
line 2 and line 3
line 1 and line 3
line 1 and line 4

In the given diagram, the lines \(\ell_1\), \(\ell_2\), \(\ell_3\), \(\ell_4\), and \(\ell_5\) represent different straight lines associated with a 3D object (a box). To identify pairs of intersecting lines, we need to examine their geometric relationships.

### Analysis:
- **Lines \(\ell_3\) and \(\ell_5\)**: These lines lie on two different planes and do not appear to intersect. So, they are **not** intersecting.
- **Lines \(\ell_2\) and \(\ell_3\)**: These lines are parallel to each other, so they do **not** intersect.
- **Lines \(\ell_1\) and \(\ell_3\)**: These lines are also in different planes, and they are skew lines (not parallel and do not intersect).
- **Lines \(\ell_1\) and \(\ell_4\)**: These two lines meet at the right edge of the box (where \(\ell_4\) is vertical and \(\ell_1\) is diagonal). Hence, **\(\ell_1\) and \(\ell_4\) intersect**.

### Conclusion:
The pair of intersecting lines is **line 1 (\(\ell_1\)) and line 4 (\(\ell_4\))**.

Would you like any further details or clarification?

Here are 5 related questions to consider:
1. What are skew lines, and how do they differ from intersecting lines?
2. Can parallel lines in 3D ever intersect?
3. How can we determine if two lines in 3D space will intersect?
4. What are the conditions for two lines to be perpendicular in 3D geometry?
5. How can vectors be used to describe lines and find intersections in space?

**Tip**: In 3D geometry, lines can be classified as parallel, intersecting, or skew. Skew lines are non-parallel and do not intersect since they lie on different planes.

Identify one pair of intersecting lines in the diagram:
line 3 and line 5
line 2 and line 3
line 1 and line 3
line 1 and line 4

This problem explores identifying intersecting lines in a 3D geometry diagram. The correct answer is line 1 (ℓ1) and line 4 (ℓ4) intersecting. This exercise focuses on understanding the relationships between lines in three-dimensional space, including skew and parallel lines. Suitable for Grades 10-12.

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