__maths__>__Properties of Vector Arithmetics__>__Properties of Dot Product__### Distributive Property over Vector Addition

In this page, learn about the distributive property of vector dot product over vector addition.

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What does 'distributive' mean?

- to share; to spread
- to share; to spread
- to restrict; to arrest

The answer is 'to share; to spread'

Given the definition of dot product as

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

What is `vec p cdot (vec q+vec r)`

- `vec p cdot ((q_x+r_x)i+(q_y+r_y)j+(q_z+r_z)k)`
- `p_x(q_x+r_x)+p_y(q_y+r_y)+p_z(q_z+r_z)`
- `vec p cdot vec q + vec p cdot vec r`
- all the above
- all the above

The answer is 'all the above'.

• Dot product of sum of vectors is sum of dot products with the vectors - Distributive.

**Distributive Property: ** For any given vectors `vec p, vec q, vec r in bbb V`

`color(coral)(vec p) cdot (vec q + vec r) = color(coral)(vec p) cdot vec q + color(coral)(vec p) cdot vec r`

*Solved Exercise Problem: *

If the dot products of two vectors `vec a` and `vec b` with a third vector `vec c` are `2` and `3`, what is `vec c cdot (vec a + vec b)` ?

- `5`
- `5`
- `6`
- `2/3`
- `3/2`

Answer is '`5`'.

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