A vector has both direction and magnitude.

## Equal vectors

2 vectors are equal to each other when they have the same direction and same magnitude. 2 vectors are said to be equal if:

- they are parallel and point in the same direction AND
- they have the same magnitude (or length)

## Addition of vectors

When we add vectors we find the resultant magnitude and direction. 2 vectors can be added using the triangle rule. To do add 2 vectors using the triangle method:

- we need to arrange the vectors such that they “continue” from one another.
- next join the “start” and “end” together
- this will give us the sum of the 2 vectors.

For instance, given the vectors **a** and **b** as shown below, draw a vector to represent **a**+**b**.

Adding vector **a** to **b** by triangle rule gives **a+b**:

## Negative vectors

When we put a negative sign in front of a vector, we reverse its direction.

For instance, in the diagram below, the difference between **a** and –**a** is the direction of the arrow.

## Multiplying a vector by a constant

Multiplying a vector by a positive constant, k, will change its magnitude to k times its original, without changing its direction.

The diagram below shows the vectors **c**, 2**c**, 3**c** and ½ **c**. All these vectors are all parallel to one another. The magnitude (length) of 2**c** is twice that of **c**, the magnitude (length) of 3**c** is thrice that of **c**, and the magnitude (length) of ½**c** is half that of **c**.

Multiplying a vector by a negative constant, -k, will reverse the direction of the constant, and its magnitude becomes k times its original.

The diagram below shows that vectors **c** and -2**c**. Observe that these 2 vectors are:

- parallel to each other
- direction of -2
**c**is the reverse of that of**c** - magnitude of -2
**c**is twice that of**c**

## Notes on H2 Math Vectors

You’ll find all the notes on H2 A Level Math Vectors topic here.

## All the notes for H2 A Level Math

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