# Vectors

A vector has both a size and a direction. It is written as a column of numbers showing the move across and up.

Maths (school) · Part 07: Shape and space · Card 8 of 9 · Last updated 2026-10-19

## Analogy

Like a treasure map instruction: 'go 3 steps east and 2 steps north'.

## Example

**a = (3, 2), b = (1, 4)**

a + b = (4, 6)
2a = (6, 4)
b - a = (-2, 2)

## In practice

Wind, force and a boat's course across a river are all vectors.

## Practice

### Flashcards

- **Add the vectors (3, 2) and (1, 4).** (4, 6).

## Questions people ask

### How do you add two vectors?

Add the top numbers together and add the bottom numbers together. For (3, 2) + (1, 4), you get (3 + 1, 2 + 4) = (4, 6). It is the same as doing one move after the other. Subtraction works in the same way: take the matching numbers away from each other instead.

### What does multiplying a vector by a number do?

It stretches or shrinks the vector, but keeps its direction. Multiply both numbers by the scalar. So 2 x (3, 2) = (6, 4), which is twice as long. A negative number also reverses the direction. Dividing by a number works the same way and shrinks the vector instead.

## Related concepts

- [Congruent shapes](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-5)
- [Similar shapes](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-6)
- [Bearings](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-7)
- [Constructions](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-9)

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