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IB Mathematics: Applications and Interpretation HL · AHL 4: Vectors · AHL 4.7
Collinear points and parallel lines with vectors Problem set B Answers
Skills
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\(\overrightarrow{PT}=\frac{3}{2}\overrightarrow{PS}\), and they share P, so P, S, T are collinear
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\(\overrightarrow{XY}=\frac{1}{2}\overrightarrow{OB}\), so they are parallel
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\(\overrightarrow{PR}=2\overrightarrow{PQ}\), so the points are collinear
In context
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\(\overrightarrow{AE}=4\overrightarrow{AD}\), and they share A, so A, D, E are collinear
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\(\overrightarrow{NH}=\overrightarrow{ML}\), so NH is parallel to ML
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\(\overrightarrow{DF}=3\overrightarrow{DE}\), so the points are collinear
Stretch
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\(k=\frac{1}{2}\)
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\(\overrightarrow{XP}=2\overrightarrow{WZ}\), so they are parallel
jmaths.xyz · AI HL · AHL 4.7 Collinear points and parallel lines with vectors