__maths__>__Properties of Vector Arithmetics__>__Properties of Dot Product__### Dot Product: Commutative Property

In this page, you will learn about the commutative property of vector dot product.

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What does 'commute' mean?

- to go to and fro on a regular basis
- to go to and fro on a regular basis
- different

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

Given the definition of dot product as

`vec p cdot vec q = |vec p||vec q|cos theta`

What is `vec q cdot vec p`?

- `vec p cdot vec q`
- `|p||q|cos(theta)`
- `|p||q|cos(-theta)`
- all the above
- all the above

The answer is 'All the above' Note that `cos(-theta) = cos(theta)`.

Given the definition of dot product as

`vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z`

What is `vec q cdot vec p`?

- `vec p cdot vec q`
- `q_xp_x+q_yp_y+q_zp_z`
- `p_xq_x+p_yq_y+p_zq_z`
- all the above
- all the above

The answer is 'All the above'

• Vectors can be swapped in dot product - commutative.

**Commutative Property of Dot Product: ** For any vector `vec p, vec q in bbb V`

`vec p cdot vec q =vec q cdot vec p`

*Solved Exercise Problem: *

Given that `vec p cdot vec q = 2.1i-1.7j+6k`, find the `vec q cdot vec p`.

- `-2.1i+1.7j-6k`
- `2.1i-1.7j+6k`
- `2.1i-1.7j+6k`
- `sqrt(2.1^2+1.7^2+6^2)`
- `2.1^2+1.7^2+6^2`

The answer is '`2.1i-1.7j+6k`' as dot product is commutative.

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