Classifying lines: parallel, intersecting, skew
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Flip to reveal answersWhat are the three ways two lines can sit in 3D?
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All 8 Flashcards — Classifying lines: parallel, intersecting, skew
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Question
What are the three ways two lines can sit in 3D?
Answer
Parallel (same direction), intersecting (meet at one point), or skew (not parallel and never meet).
Question
How do you check if two lines are parallel?
Answer
See if one direction vector is a scalar multiple of the other: d₂ = k·d₁.
Question
What is a skew pair of lines?
Answer
Lines that are NOT parallel and yet NEVER meet — only possible in 3D.
Question
How do you find the intersection of two lines?
Answer
Equate the position vectors (3 component equations), solve two for s and t, then test the third; if it holds, sub s back for the point.
Question
Why solve only two of the three equations?
Answer
Two equations fix s and t; the third is the consistency check — it tells you whether the lines actually meet.
Question
How do you prove two lines are skew?
Answer
Show the directions are NOT parallel AND the equation system is inconsistent (no common s, t).
Question
Is 'the lines never meet' enough to call them skew?
Answer
No — parallel lines also never meet. You must also show the directions are not parallel.
Question
Lines perpendicular and intersecting: how do you find unknown constants?
Answer
Perpendicularity (dot product = 0) gives a direction unknown; forcing the intersection (third equation) gives a position unknown.
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Full study notes for Classifying lines: parallel, intersecting, skew
Topic 3.15 hub
Classifying lines (HL only)
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