Pure · Vectors
Chapter 1 · 4
The idea
Vector notation and representation
What a vector is (a size and a direction), the ways we write one (bold letter, arrow, column, i–j components), and how to add, subtract and scale vectors — both geometrically (nose-to-tail) and component by component.
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
Pure · Vectors
Vector notation and representation
What a vector is (a size and a direction), the ways we write one (bold letter, arrow, column, i–j components), and how to add, subtract and scale vectors — both geometrically (nose-to-tail) and component by component.
Why it works
A size and a direction
A scalar is just a size — , , a temperature. A vector carries a size and a direction: a displacement of " km north-east", a velocity, a force. We draw one as an arrow (a directed line segment): its length is the magnitude and the way it points is the direction.Four ways to write one
- a bold letter (handwritten: underlined, );
- an arrow between two points, — "from to ";
- a column, ;
- in terms of the unit vectors (one unit along the -axis) and (one unit along the -axis): .
Keep reading — free
The rest of the explanation, plus 4 worked examples you step through move by move.
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