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Vectors: magnitude, direction and products

Divide a segment in a stated ratio · Diagrams · Complete reading

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Ratio theorem with a common reference

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Two schematic triangles have the same A,P,B order with AP:PB=λ:μ. Their common starting point is O in one panel and C in the other. Rays to A,P,B are directed from that common reference. Equal λ and μ give the midpoint.
Two schematic triangles have the same A,P,B order with AP:PB=λ:μ. Their common starting point is O in one panel and C in the other. Rays to A,P,B are directed from that common reference. Equal λ and μ give the midpoint.
Two schematic triangles have the same A,P,B order with AP:PB=λ:μ. Their common starting point is O in one panel and C in the other. Rays to A,P,B are directed from that common reference. Equal λ and μ give the midpoint.
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Five source cases: Example 5 has A,P,B with lengths 3,7; B,A,R with BA=5, AR=2, BR=7; A,B,Q with AB=4, BQ=3, AQ=7. Example 6 has A,P,B with AP=2, PB=3 and A,B,P with AB=BP=1. Position rays start at O in the Example 6 panels. Segment ratios, not added coordinate axes, set these schematic layouts.
Five source cases: Example 5 has A,P,B with lengths 3,7; B,A,R with BA=5, AR=2, BR=7; A,B,Q with AB=4, BQ=3, AQ=7. Example 6 has A,P,B with AP=2, PB=3 and A,B,P with AB=BP=1. Position rays start at O in the Example 6 panels. Segment ratios, not added coordinate axes, set these schematic layouts.
Five source cases: Example 5 has A,P,B with lengths 3,7; B,A,R with BA=5, AR=2, BR=7; A,B,Q with AB=4, BQ=3, AQ=7. Example 6 has A,P,B with AP=2, PB=3 and A,B,P with AB=BP=1. Position rays start at O in the Example 6 panels. Segment ratios, not added coordinate axes, set these schematic layouts.
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