Video: Relation between Straight Lines

Using the cube below, decide which of the following describe the relative position of the straight lines 𝐴𝐵 and 𝐷𝐷′. [A] Parallel [B] Perpendicular [C] Intersecting [D] Skew.

01:27

Video Transcript

Using the cube below, decide which of the following describe the relative position of the straight lines 𝐴𝐵 and 𝐷𝐷 prime: parallel, perpendicular, intersecting, or skew.

So, we begin by highlighting the two lines of interest: the line 𝐴𝐵 and 𝐷𝐷 prime. Let’s now consider each of these different options in turn. We can see from the diagram that the two lines are not in the same plane. They’re not coplanar.

This automatically rules out two of the possibilities. In order for two lines to be either parallel or perpendicular, they need to be in the same plane. So we’re left with either intersecting or skew.

From the diagram, we can see that these two lines do not intersect. Therefore, the only remaining possibility is that these two lines are skew. Let’s recall the definition of what it means for two lines to be skew.

Two lines are skew if firstly they are not coplanar and secondly if they do not intersect. We’ve already shown both of these conditions to be true of the two lines in question. Therefore, the relative position of the straight lines 𝐴𝐵 and 𝐷𝐷 prime is that they are skew.

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