Geometry & measures · Vectors
Chapter 1 · 3
The idea
Vectors on a shape
Expressing any journey around a figure in terms of two given vectors — why every route gives the same answer, why going against an arrow flips the sign, and why a point splitting a side in the ratio 2:3 sits two fifths along, not two thirds.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Geometry & measures · Vectors
Vectors on a shape
Expressing any journey around a figure in terms of two given vectors — why every route gives the same answer, why going against an arrow flips the sign, and why a point splitting a side in the ratio 2:3 sits two fifths along, not two thirds.
Why it works
The same vector, anywhere on the shape
A vector is a journey, not a place. It records two things and only two things — how far, and in which direction. It records nothing about where the journey started. That one fact is the engine of this whole topic, because it means the same vector can appear in several different places on the same diagram. In a parallelogram with , the opposite side is the same length as and points the same way, so as well. Not "something like " — the very same vector, written with the very same letter.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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