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

In this page, learn about the distributive property of vector cross 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 cross product as

`vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|`

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

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

The answer is 'all the above'.

• Cross product of sum of vectors is sum of cross products with the vectors - Distributive.

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

`vec p xx (vec q + vec r) = vec p xx vec q + vec p xx vec r`

*Solved Exercise Problem: *

If the cross products of `vec c` with two vectors `vec a` and `vec b` are `2` and `3`, what is `vec c xx (vec a + vec b)` ?

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

Answer is '`5`'.

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