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

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

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What does 'Associate' mean?

- to connect with; to join
- to connect with; to join
- not to connect

The answer is 'to connect with; to join'

When three vectors are added,

• Person A *associates* the middle vector with first vector and, to the result of that, he adds the third vector `(vec a + vec b) + vec c`

• Person B *associates* the middle vector with third vector and to that she adds the first vector `vec a + (vec b + vec c)` Will the two persons get different results?

- They will get different results
- They will get identical results
- They will get identical results

The answer is 'They will get identical results'. Considering that the components of vectors are real numbers, the order of additions does not change the result of addition.

• Order of addition can be changed - associative.

**Associative Property of Vector Addition: ** Any vectors `vec a, vec b, vec c in bbb V`,

`(vec a+vec b)+vec c`

`quad quad = vec a + (vec b + vec c)`

*Solved Exercise Problem: *

Which of the following equals `vec x + vec y + vec x`?

- `vec x + vec y`
- `vec x + vec x + vec y`
- `vec x + vec x + vec y`
- `vec y + vec x`
- `vec y + vec y + vec x`

The answer is '`vec x + vec x + vec y`'

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