__maths__>__Properties of Vector Arithmetics__>__Properties of Vector Addition__### Commutative Property of Vector Addition

In this page, commutative property of vector addition is explained.

*click on the content to continue..*

What does 'commute' mean?

- to go to and fro on a regular basis
- to go to and fro on a regular basis
- is it an English word?

The answer is 'to go to and fro between two places on a regular basis'.

Vector addition is the addition of components. The components are real numbers. If the vectors are swapped in a vector addition, will the sum be same?

- the result will be same
- the result will be same
- the result will change

The answer is 'the result will be same'. The real numbers are commutative. The components of vectors are real numbers and so vectors are commutative.

• Vectors can be swapped in vector addition - commutative.

**Commutative Property of Vector Addition: ** For any vector `vec a, vec b in bbb V`

`vec a+vec b =vec b + vec a`

*Solved Exercise Problem: *

Given that `vec p + vec q = 2i-1.2j+.5k`, Which one of the following is `vec q + vec p`?.

- `.5i-1.2j+2k`
- `.5i+2j-1.2k`
- `2i-1.2j+.5k`
- `2i-1.2j+.5k`
- `-1.2i+.5j+2k`

The answer is '`2i-1.2j+.5k`', since vector addition is commutative.

*slide-show version coming soon*